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Axioms
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Mathematical Analysis and Applications II
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Mathematical Analysis and Applications II

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (30 November 2019) | Viewed by 54220

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Prof. Dr. Hari Mohan Srivastava

grade E-Mail Website
Guest Editor
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Interests: real and complex analysis; fractional calculus and its applications; integral equations and transforms; higher transcendental functions and their applications; q-series and q-polynomials; analytic number theory; analytic and geometric Inequalities; probability and statistics; inventory modeling and optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This issue is a continuation of the previous successful Special Issue “Mathematical Analysis and Applications”.

Investigations involving the theory and applications of mathematical analytical tools and techniques are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. In this Special Issue, we invite and welcome review, expository and original research articles dealing with the recent advances in mathematical analysis and its multidisciplinary applications.

We look forward to your contributions to this Special Issue.

Best wishes,

Prof. Dr. Hari Mohan Srivastava
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Mathematical (or Higher Transcendental) Functions and Their Applications
  • Fractional Calculus and Its Applications
  • q-Series and q-Polynomials
  • Analytic Number Theory
  • Special Functions of Mathematical Physics and Applied Mathematics
  • Geometric Function Theory of Complex Analysis

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Published Papers (18 papers)

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Editorial

Jump to: Research, Review

3 pages, 190 KiB  
Editorial
Mathematical Analysis and Applications II
by Hari M. Srivastava
Axioms 2020, 9(1), 16; https://doi.org/10.3390/axioms9010016 - 06 Feb 2020
Viewed by 1867
Abstract
Web Site: http://www [...] Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)

Research

Jump to: Editorial, Review

9 pages, 266 KiB  
Article
Repeated Derivatives of Hyperbolic Trigonometric Functions and Associated Polynomials
by Giuseppe Dattoli, Silvia Licciardi, Rosa Maria Pidatella and Elio Sabia
Axioms 2019, 8(4), 138; https://doi.org/10.3390/axioms8040138 - 06 Dec 2019
Cited by 1 | Viewed by 2650
Abstract
Elementary problems as the evaluation of repeated derivatives of ordinary transcendent functions can usefully be treated with the use of special polynomials and of a formalism borrowed from combinatorial analysis. Motivated by previous researches in this field, we review the results obtained by [...] Read more.
Elementary problems as the evaluation of repeated derivatives of ordinary transcendent functions can usefully be treated with the use of special polynomials and of a formalism borrowed from combinatorial analysis. Motivated by previous researches in this field, we review the results obtained by other authors and develop a complementary point of view for the repeated derivatives of sec ( . ) , tan ( . ) and for their hyperbolic counterparts. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
13 pages, 266 KiB  
Article
Approximation Properties of an Extended Family of the Szász–Mirakjan Beta-Type Operators
by Hari Mohan Srivastava, Gürhan İçöz and Bayram Çekim
Axioms 2019, 8(4), 111; https://doi.org/10.3390/axioms8040111 - 10 Oct 2019
Cited by 27 | Viewed by 3053
Abstract
Approximation and some other basic properties of various linear and nonlinear operators are potentially useful in many different areas of researches in the mathematical, physical, and engineering sciences. Motivated essentially by this aspect of approximation theory, our present study systematically investigates the approximation [...] Read more.
Approximation and some other basic properties of various linear and nonlinear operators are potentially useful in many different areas of researches in the mathematical, physical, and engineering sciences. Motivated essentially by this aspect of approximation theory, our present study systematically investigates the approximation and other associated properties of a class of the Szász-Mirakjan-type operators, which are introduced here by using an extension of the familiar Beta function. We propose to establish moments of these extended Szász-Mirakjan Beta-type operators and estimate various convergence results with the help of the second modulus of smoothness and the classical modulus of continuity. We also investigate convergence via functions which belong to the Lipschitz class. Finally, we prove a Voronovskaja-type approximation theorem for the extended Szász-Mirakjan Beta-type operators. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
12 pages, 277 KiB  
Article
Slice Holomorphic Functions in Several Variables with Bounded L-Index in Direction
by Andriy Bandura and Oleh Skaskiv
Axioms 2019, 8(3), 88; https://doi.org/10.3390/axioms8030088 - 26 Jul 2019
Cited by 14 | Viewed by 2693
Abstract
In this paper, for a given direction b ∈ C n \ { 0 } we investigate slice entire functions of several complex variables, i.e., we consider functions which are entire on a complex line [...] Read more.
In this paper, for a given direction b ∈ C n \ { 0 } we investigate slice entire functions of several complex variables, i.e., we consider functions which are entire on a complex line { z 0 + t b : t ∈ C } for any z 0 ∈ C n . Unlike to quaternionic analysis, we fix the direction b . The usage of the term slice entire function is wider than in quaternionic analysis. It does not imply joint holomorphy. For example, it allows consideration of functions which are holomorphic in variable z 1 and continuous in variable z 2 . For this class of functions there is introduced a concept of boundedness of L-index in the direction b where L : C n → R + is a positive continuous function. We present necessary and sufficient conditions of boundedness of L-index in the direction. In this paper, there are considered local behavior of directional derivatives and maximum modulus on a circle for functions from this class. Also, we show that every slice holomorphic and joint continuous function has bounded L-index in direction in any bounded domain and for any continuous function L : C n → R + . Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
21 pages, 312 KiB  
Article
On a New Class of Laplace-Type Integrals Involving Generalized Hypergeometric Functions
by Wolfram Koepf, Insuk Kim and Arjun K. Rathie
Axioms 2019, 8(3), 87; https://doi.org/10.3390/axioms8030087 - 26 Jul 2019
Cited by 12 | Viewed by 3336
Abstract
In the theory of generalized hypergeometric functions, classical summation theorems for the series 2 F 1 , 3 F 2 , 4 F 3 , 5 F 4 and 7 F 6 play a key role. Very recently, Masjed-Jamei and Koepf established generalizations [...] Read more.
In the theory of generalized hypergeometric functions, classical summation theorems for the series 2 F 1 , 3 F 2 , 4 F 3 , 5 F 4 and 7 F 6 play a key role. Very recently, Masjed-Jamei and Koepf established generalizations of the above-mentioned summation theorems. Inspired by their work, the main objective of the paper is to provide a new class of Laplace-type integrals involving generalized hypergeometric functions p F p for p = 2 , 3 , 4 , 5 and 7 in the most general forms. Several new and known cases have also been obtained as special cases of our main findings. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
11 pages, 258 KiB  
Article
Generalized Hyers–Ulam Stability of the Additive Functional Equation
by Yang-Hi Lee and Gwang Hui Kim
Axioms 2019, 8(2), 76; https://doi.org/10.3390/axioms8020076 - 25 Jun 2019
Cited by 4 | Viewed by 2901
Abstract
We will prove the generalized Hyers–Ulam stability and the hyperstability of the additive functional equation f(x1 + y1, x2 + y2, …, xn + yn) = f(x1, x [...] Read more.
We will prove the generalized Hyers–Ulam stability and the hyperstability of the additive functional equation f(x1 + y1, x2 + y2, …, xn + yn) = f(x1, x2, … xn) + f(y1, y2, …, yn). By restricting the domain of a mapping f that satisfies the inequality condition used in the assumption part of the stability theorem, we partially generalize the results of the stability theorems of the additive function equations. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
12 pages, 276 KiB  
Article
On Almost b-Metric Spaces and Related Fixed Point Results
by Nabil Mlaiki, Katarina Kukić, Milanka Gardašević-Filipović and Hassen Aydi
Axioms 2019, 8(2), 70; https://doi.org/10.3390/axioms8020070 - 01 Jun 2019
Cited by 9 | Viewed by 3256
Abstract
In this manuscript, we introduce almost b-metric spaces and prove modifications of fixed point theorems for Reich and Hardy–Rogers type contractions. We present an approach generalizing some fixed point theorems to the case of almost b-metric spaces by reducing almost b [...] Read more.
In this manuscript, we introduce almost b-metric spaces and prove modifications of fixed point theorems for Reich and Hardy–Rogers type contractions. We present an approach generalizing some fixed point theorems to the case of almost b-metric spaces by reducing almost b-metrics to the corresponding b-metrics. Later, we show that this approach can not work for all kinds of contractions. To confirm this, we present a proof in which the contraction condition is such that it cannot be reduced to corresponding b-metrics. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
10 pages, 774 KiB  
Article
(p, q)-Hermite–Hadamard Inequalities for Double Integral and (p, q)-Differentiable Convex Functions
by Julalak Prabseang, Kamsing Nonlaopon and Jessada Tariboon
Axioms 2019, 8(2), 68; https://doi.org/10.3390/axioms8020068 - 28 May 2019
Cited by 19 | Viewed by 3081
Abstract
The aim of this paper is to establish some new ( p , q ) -calculus of Hermite–Hadamard inequalities for the double integral and refinements of the Hermite–Hadamard inequality for ( p , q ) -differentiable convex functions. [...] Read more.
The aim of this paper is to establish some new ( p , q ) -calculus of Hermite–Hadamard inequalities for the double integral and refinements of the Hermite–Hadamard inequality for ( p , q ) -differentiable convex functions. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
12 pages, 276 KiB  
Article
Some New Results Involving the Generalized Bose–Einstein and Fermi–Dirac Functions
by Rekha Srivastava, Humera Naaz, Sabeena Kazi and Asifa Tassaddiq
Axioms 2019, 8(2), 63; https://doi.org/10.3390/axioms8020063 - 21 May 2019
Cited by 2 | Viewed by 2900
Abstract
In this paper, we obtain a new series representation for the generalized Bose–Einstein and Fermi–Dirac functions by using fractional Weyl transform. To achieve this purpose, we obtain an analytic continuation for these functions by generalizing the domain of Riemann zeta functions from [...] Read more.
In this paper, we obtain a new series representation for the generalized Bose–Einstein and Fermi–Dirac functions by using fractional Weyl transform. To achieve this purpose, we obtain an analytic continuation for these functions by generalizing the domain of Riemann zeta functions from ( 0 < ℜ ( s ) < 1 ) to ( 0 < ℜ ( s ) < μ ) . This leads to fresh insights for a new generalization of the Riemann zeta function. The results are validated by obtaining the classical series representation of the polylogarithm and Hurwitz–Lerch zeta functions as special cases. Fractional derivatives and the relationship of the generalized Bose–Einstein and Fermi–Dirac functions with Apostol–Euler–Nörlund polynomials are established to prove new identities. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
10 pages, 262 KiB  
Article
A Short Note on Integral Transformations and Conversion Formulas for Sequence Generating Functions
by Maxie D. Schmidt
Axioms 2019, 8(2), 62; https://doi.org/10.3390/axioms8020062 - 19 May 2019
Cited by 1 | Viewed by 3899
Abstract
The purpose of this note is to provide an expository introduction to some more curious integral formulas and transformations involving generating functions. We seek to generalize these results and integral representations which effectively provide a mechanism for converting between a sequence’s ordinary and [...] Read more.
The purpose of this note is to provide an expository introduction to some more curious integral formulas and transformations involving generating functions. We seek to generalize these results and integral representations which effectively provide a mechanism for converting between a sequence’s ordinary and exponential generating function (OGF and EGF, respectively) and vice versa. The Laplace transform provides an integral formula for the EGF-to-OGF transformation, where the reverse OGF-to-EGF operation requires more careful integration techniques. We prove two variants of the OGF-to-EGF transformation integrals from the Hankel loop contour for the reciprocal gamma function and from Fourier series expansions of integral representations for the Hadamard product of two generating functions, respectively. We also suggest several generalizations of these integral formulas and provide new examples along the way. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
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12 pages, 260 KiB  
Article
Fixed Point Theorems through Modified ω-Distance and Application to Nontrivial Equations
by Tariq Qawasmeh, Abdalla Tallafha and Wasfi Shatanawi
Axioms 2019, 8(2), 57; https://doi.org/10.3390/axioms8020057 - 08 May 2019
Cited by 17 | Viewed by 2764
Abstract
In this manuscript, we utilize the concept of modified ω -distance mapping, which was introduced by Alegre and Marin [Alegre, C.; Marin, J. Modified ω -distance on quasi metric spaces and fixed point theorems on complete quasi metric spaces. Topol. Appl. 2016, [...] Read more.
In this manuscript, we utilize the concept of modified ω -distance mapping, which was introduced by Alegre and Marin [Alegre, C.; Marin, J. Modified ω -distance on quasi metric spaces and fixed point theorems on complete quasi metric spaces. Topol. Appl. 2016, 203, 120–129] in 2016 to introduce the notions of ( ω , φ ) -Suzuki contraction and generalized ( ω , φ ) -Suzuki contraction. We employ these notions to prove some fixed point results. Moreover, we introduce an example to show the novelty of our results. Furthermore, we introduce some applications for our results. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
6 pages, 257 KiB  
Article
A Note on the Displacement Problem of Elastostatics with Singular Boundary Values
by Alfonsina Tartaglione
Axioms 2019, 8(2), 46; https://doi.org/10.3390/axioms8020046 - 19 Apr 2019
Cited by 4 | Viewed by 2262
Abstract
The displacement problem of linear elastostatics in bounded and exterior domains with a non-regular boundary datum a is considered. Precisely, if the elastic body is represented by a domain of class C k ( k ≥ 2 ) of R 3 and [...] Read more.
The displacement problem of linear elastostatics in bounded and exterior domains with a non-regular boundary datum a is considered. Precisely, if the elastic body is represented by a domain of class C k ( k ≥ 2 ) of R 3 and a ∈ W 2 − k − 1 / q , q ( ∂ Ω ) , q ∈ ( 1 , + ∞ ) , then it is proved that there exists a solution which is of class C ∞ in the interior and takes the boundary value in a well-defined sense. Moreover, it is unique in a natural function class. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
15 pages, 258 KiB  
Article
Fixed Point Results in Partial Symmetric Spaces with an Application
by Mohammad Asim, A. Rauf Khan and Mohammad Imdad
Axioms 2019, 8(1), 13; https://doi.org/10.3390/axioms8010013 - 22 Jan 2019
Cited by 13 | Viewed by 2924
Abstract
In this paper, we first introduce the class of partial symmetric spaces and then prove some fixed point theorems in such spaces. We use one of the our main results to examine the existence and uniqueness of a solution for a system of [...] Read more.
In this paper, we first introduce the class of partial symmetric spaces and then prove some fixed point theorems in such spaces. We use one of the our main results to examine the existence and uniqueness of a solution for a system of Fredholm integral equations. Furthermore, we introduce an analogue of the Hausdorff metric in the context of partial symmetric spaces and utilize the same to prove an analogue of the Nadler contraction principle in such spaces. Our results extend and improve many results in the existing literature. We also give some examples exhibiting the utility of our newly established results. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
9 pages, 217 KiB  
Article
A New Identity for Generalized Hypergeometric Functions and Applications
by Mohammad Masjed-Jamei and Wolfram Koepf
Axioms 2019, 8(1), 12; https://doi.org/10.3390/axioms8010012 - 18 Jan 2019
Cited by 5 | Viewed by 2975
Abstract
We establish a new identity for generalized hypergeometric functions and apply it for first- and second-kind Gauss summation formulas to obtain some new summation formulas. The presented identity indeed extends some results of the recent published paper (Some summation theorems for generalized [...] Read more.
We establish a new identity for generalized hypergeometric functions and apply it for first- and second-kind Gauss summation formulas to obtain some new summation formulas. The presented identity indeed extends some results of the recent published paper (Some summation theorems for generalized hypergeometric functions, Axioms, 7 (2018), Article 38). Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
9 pages, 221 KiB  
Article
Extended Partial Sb-Metric Spaces
by Aiman Mukheimer
Axioms 2018, 7(4), 87; https://doi.org/10.3390/axioms7040087 - 21 Nov 2018
Cited by 4 | Viewed by 3038
Abstract
In this paper, we introduce the concept of extended partial S b -metric spaces, which is a generalization of the extended S b -metric spaces. Basically, in the triangle inequality, we add a control function with some very interesting properties. These new metric [...] Read more.
In this paper, we introduce the concept of extended partial S b -metric spaces, which is a generalization of the extended S b -metric spaces. Basically, in the triangle inequality, we add a control function with some very interesting properties. These new metric spaces generalize many results in the literature. Moreover, we prove some fixed point theorems under some different contractions, and some examples are given to illustrate our results. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
10 pages, 240 KiB  
Article
On the Fixed-Circle Problem and Khan Type Contractions
by Nabil Mlaiki, Nihal Taş and Nihal Yılmaz Özgür
Axioms 2018, 7(4), 80; https://doi.org/10.3390/axioms7040080 - 08 Nov 2018
Cited by 32 | Viewed by 3327
Abstract
In this paper, we consider the fixed-circle problem on metric spaces and give new results on this problem. To do this, we present three types of F C -Khan type contractions. Furthermore, we obtain some solutions to an open problem related to the [...] Read more.
In this paper, we consider the fixed-circle problem on metric spaces and give new results on this problem. To do this, we present three types of F C -Khan type contractions. Furthermore, we obtain some solutions to an open problem related to the common fixed-circle problem. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
17 pages, 789 KiB  
Article
Common Fixed Point Theorems for Generalized Geraghty (α,ψ,ϕ)-Quasi Contraction Type Mapping in Partially Ordered Metric-Like Spaces
by Haitham Qawaqneh, Mohd Noorani, Wasfi Shatanawi and Habes Alsamir
Axioms 2018, 7(4), 74; https://doi.org/10.3390/axioms7040074 - 25 Oct 2018
Cited by 14 | Viewed by 3414
Abstract
The aim of this paper is to establish the existence of some common fixed point results for generalized Geraghty ( α , ψ , ϕ ) -quasi contraction self-mapping in partially ordered metric-like spaces. We display an example and an application to show [...] Read more.
The aim of this paper is to establish the existence of some common fixed point results for generalized Geraghty ( α , ψ , ϕ ) -quasi contraction self-mapping in partially ordered metric-like spaces. We display an example and an application to show the superiority of our results. The obtained results progress some well-known fixed (common fixed) point results in the literature. Our main results cannot be specifically attained from the corresponding metric space versions. This paper is scientifically novel because we take Geraghty contraction self-mapping in partially ordered metric-like spaces via α − admissible mapping. This opens the door to other possible fixed (common fixed) point results for non-self-mapping and in other generalizing metric spaces. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)

Review

Jump to: Editorial, Research

15 pages, 238 KiB  
Review
Differential Equations for Classical and Non-Classical Polynomial Sets: A Survey
by Paolo Emilio Ricci
Axioms 2019, 8(2), 50; https://doi.org/10.3390/axioms8020050 - 25 Apr 2019
Cited by 2 | Viewed by 2629
Abstract
By using the monomiality principle and general results on Sheffer polynomial sets, the differential equation satisfied by several old and new polynomial sets is shown. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
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