Research

14 pages, 504 KiB

Open AccessFeature PaperArticle

Fast Computation of Integrals with Fourier-Type Oscillator Involving Stationary Point

by Sakhi Zaman, Irshad Hussain and Dhananjay Singh

Mathematics 2019, 7(12), 1160; https://doi.org/10.3390/math7121160 - 02 Dec 2019

Cited by 17 | Viewed by 2044

An adaptive splitting algorithm was implemented for numerical evaluation of Fourier-type highly oscillatory integrals involving stationary point. Accordingly, a modified Levin collocation method was coupled with multi-resolution quadratures in order to tackle the stationary point and irregular oscillations of the integrand caused by [...] Read more.

An adaptive splitting algorithm was implemented for numerical evaluation of Fourier-type highly oscillatory integrals involving stationary point. Accordingly, a modified Levin collocation method was coupled with multi-resolution quadratures in order to tackle the stationary point and irregular oscillations of the integrand caused by

ω

. Some test problems are included to verify the accuracy of the proposed methods. Full article

(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)

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15 pages, 282 KiB

Open AccessArticle

Extended Rectangular M_rξ-Metric Spaces and Fixed Point Results

by Mohammad Asim, Kottakkaran Sooppy Nisar, Ahmed Morsy and Mohammad Imdad

Mathematics 2019, 7(12), 1136; https://doi.org/10.3390/math7121136 - 21 Nov 2019

Cited by 6 | Viewed by 1718

Abstract

In this paper, we enlarge the classes of rectangular

M_{b}

-metric spaces and extended rectangular b-metric spaces by considering the class of extended rectangular

M_{r ξ}

-metric spaces and utilize the same to prove an analogue of Banach contraction principle [...] Read more.

In this paper, we enlarge the classes of rectangular

M_{b}

-metric spaces and extended rectangular b-metric spaces by considering the class of extended rectangular

M_{r ξ}

-metric spaces and utilize the same to prove an analogue of Banach contraction principle in such spaces. We adopt an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of solution for a system of Fredholm integral equation. Full article

(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)

11 pages, 288 KiB

Open AccessArticle

A New Fixed Point Theorem and a New Generalized Hyers-Ulam-Rassias Stability in Incomplete Normed Spaces

by Maryam Ramezani, Ozgur Ege and Manuel De la Sen

Mathematics 2019, 7(11), 1117; https://doi.org/10.3390/math7111117 - 16 Nov 2019

Cited by 3 | Viewed by 1750

Abstract

In this study, our goal is to apply a new fixed point method to prove the Hyers-Ulam-Rassias stability of a quadratic functional equation in normed spaces which are not necessarily Banach spaces. The results of the present paper improve and extend some previous [...] Read more.

In this study, our goal is to apply a new fixed point method to prove the Hyers-Ulam-Rassias stability of a quadratic functional equation in normed spaces which are not necessarily Banach spaces. The results of the present paper improve and extend some previous results. Full article

(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)

16 pages, 286 KiB

Open AccessFeature PaperArticle

On Common Fixed Point Results for New Contractions with Applications to Graph and Integral Equations

by Haitham Qawaqneh, Mohd Salmi Noorani, Hassen Aydi and Wasfi Shatanawi

Mathematics 2019, 7(11), 1082; https://doi.org/10.3390/math7111082 - 09 Nov 2019

Cited by 2 | Viewed by 1661

Abstract

The investigation of symmetric/asymmetric structures and their applications in mathematics (in particular in operator theory and functional analysis) is useful and fruitful. A metric space has the property of symmetry. By looking in the same direction and using the

α

-admissibility with regard [...] Read more.

The investigation of symmetric/asymmetric structures and their applications in mathematics (in particular in operator theory and functional analysis) is useful and fruitful. A metric space has the property of symmetry. By looking in the same direction and using the

α

-admissibility with regard to

η

and

θ

-functions, we demonstrate some existence and uniqueness fixed point theorems. The obtained results extend and generalize the main result of Isik et al. (2019). At the end, some illustrated applications are presented. Full article

(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)

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18 pages, 319 KiB

Open AccessArticle

A Coupled Fixed Point Technique for Solving Coupled Systems of Functional and Nonlinear Integral Equations

by Hasanen Abuelmagd Hammad and Manuel De la Sen

Mathematics 2019, 7(7), 634; https://doi.org/10.3390/math7070634 - 17 Jul 2019

Cited by 30 | Viewed by 2809

Abstract

In this paper, we obtain coupled fixed point results for F-contraction mapping satisfying a nonlinear contraction condition in the framework of complete metric space without and with a directed graph. As applications of our results, we study a problem of existence and [...] Read more.

In this paper, we obtain coupled fixed point results for F-contraction mapping satisfying a nonlinear contraction condition in the framework of complete metric space without and with a directed graph. As applications of our results, we study a problem of existence and uniqueness of solutions for a class of systems of functional equations that appears in dynamic programming and nonlinear integral equations. Finally, illustrative examples to support some our results are discussed. Full article

(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)

14 pages, 273 KiB

Open AccessArticle

Generalized (σ,ξ)-Contractions and Related Fixed Point Results in a P.M.S

by Vahid Parvaneh, Babak Mohammadi, Hassen Aydi and Aiman Mukheimer

Mathematics 2019, 7(5), 481; https://doi.org/10.3390/math7050481 - 27 May 2019

Viewed by 2197

Abstract

In this paper, we present the concept of

Θ - {(σ, ξ)}_{Ω}

-contraction mappings and we nominate some related fixed point results in ordered p-metric spaces. Our results extend several famous ones in the literature. Some examples and [...] Read more.

In this paper, we present the concept of

Θ - {(σ, ξ)}_{Ω}

-contraction mappings and we nominate some related fixed point results in ordered p-metric spaces. Our results extend several famous ones in the literature. Some examples and an application are given in order to validate our results. Full article

(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)

15 pages, 264 KiB

Open AccessArticle

A Mizoguchi–Takahashi Type Fixed Point Theorem in Complete Extended b-Metric Spaces

by Nayab Alamgir, Quanita Kiran, Hassen Aydi and Aiman Mukheimer

Mathematics 2019, 7(5), 478; https://doi.org/10.3390/math7050478 - 26 May 2019

Cited by 11 | Viewed by 3023

Abstract

In this paper, we prove a new fixed point theorem for a multi-valued mapping from a complete extended b-metric space U into the non empty closed and bounded subsets of U, which generalizes Nadler’s fixed point theorem. We also establish some [...] Read more.

In this paper, we prove a new fixed point theorem for a multi-valued mapping from a complete extended b-metric space U into the non empty closed and bounded subsets of U, which generalizes Nadler’s fixed point theorem. We also establish some fixed point results, which generalize our first result. Furthermore, we establish Mizoguchi–Takahashi’s type fixed point theorem for a multi-valued mapping from a complete extended b-metric space U into the non empty closed and bounded subsets of U that improves many existing results in the literature. Full article

(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)

8 pages, 270 KiB

Open AccessArticle

Picard-Jungck Operator for a Pair of Mappings and Simulation Type Functions

by Sumit Chandok, Aiman Mukheimer, Azhar Hussain and Ljiljana Paunović

Mathematics 2019, 7(5), 461; https://doi.org/10.3390/math7050461 - 22 May 2019

Cited by 4 | Viewed by 2104

Abstract

In this manuscript, we propose a new class of Picard-Jungck operators for a pair of mappings on complete metric spaces by taking into account of the

C_{G}

-simulation function. Also, some new results for the existence of such operators for a pair [...] Read more.

In this manuscript, we propose a new class of Picard-Jungck operators for a pair of mappings on complete metric spaces by taking into account of the

C_{G}

-simulation function. Also, some new results for the existence of such operators for a pair of self mappings in the setting of metric spaces are obtained. Some nontrivial examples are presented to show the usability of the results. Full article

(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)

11 pages, 273 KiB

Open AccessArticle

Large Contractions on Quasi-Metric Spaces with an Application to Nonlinear Fractional Differential Equations

by Erdal Karapınar, Andreea Fulga, Maliha Rashid, Lariab Shahid and Hassen Aydi

Mathematics 2019, 7(5), 444; https://doi.org/10.3390/math7050444 - 18 May 2019

Cited by 98 | Viewed by 3191

Abstract

In this manuscript, we introduce a new notion: a Berinde type

(α, ψ)

-contraction mapping. Thereafter, we investigate not only the existence, but also the uniqueness of a fixed point of such mappings in the setting of right-complete quasi-metric spaces. [...] Read more.

In this manuscript, we introduce a new notion: a Berinde type

(α, ψ)

-contraction mapping. Thereafter, we investigate not only the existence, but also the uniqueness of a fixed point of such mappings in the setting of right-complete quasi-metric spaces. The result, presented here, not only generalizes a number of existing results, but also unifies several ones on the topic in the literature. An application of nonlinear fractional differential equations is given. Full article

(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)

12 pages, 261 KiB

Open AccessArticle

Common Fixed Point Results for Rational (α,β)_φ-mω Contractions in Complete Quasi Metric Spaces

by Tariq Qawasmeh, Wasfi Shatanawi, Anwar Bataihah and Abdalla Tallafha

Mathematics 2019, 7(5), 392; https://doi.org/10.3390/math7050392 - 30 Apr 2019

Cited by 13 | Viewed by 1900

Abstract

The

ω

-distance mapping is one of the important tools that can be used to get new contractions in fixed point theory. The aim of this paper is to use the concept of modified

ω

-distance mapping to introduce the notion of rational [...] Read more.

The

ω

-distance mapping is one of the important tools that can be used to get new contractions in fixed point theory. The aim of this paper is to use the concept of modified

ω

-distance mapping to introduce the notion of rational

{(α, β)}_{φ}

-

m ω

contraction. We utilize our new notion to construct and formulate many fixed point results for a pair of two mappings defined on a nonempty set A. Our results modify many existing known results. In addition, we support our work by an example. Full article

(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)

12 pages, 366 KiB

Open AccessArticle

Weak Partial b-Metric Spaces and Nadler’s Theorem

by Tanzeela Kanwal, Azhar Hussain, Poom Kumam and Ekrem Savas

Mathematics 2019, 7(4), 332; https://doi.org/10.3390/math7040332 - 05 Apr 2019

Cited by 8 | Viewed by 2726

Abstract

The purpose of this paper is to define the notions of weak partial b-metric spaces and weak partial Hausdorff b-metric spaces along with the topology of weak partial b-metric space. Moreover, we present a generalization of Nadler’s theorem by using [...] Read more.

The purpose of this paper is to define the notions of weak partial b-metric spaces and weak partial Hausdorff b-metric spaces along with the topology of weak partial b-metric space. Moreover, we present a generalization of Nadler’s theorem by using weak partial Hausdorff b-metric spaces in the context of a weak partial b-metric space. We present a non-trivial example which show the validity of our result and an application to nonlinear Volterra integral inclusion for the applicability purpose. Full article

(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)

13 pages, 757 KiB

Open AccessArticle

Optimal Approximate Solution of Coincidence Point Equations in Fuzzy Metric Spaces

by Naeem Saleem, Mujahid Abbas and Manuel De la Sen

Mathematics 2019, 7(4), 327; https://doi.org/10.3390/math7040327 - 03 Apr 2019

Cited by 10 | Viewed by 2019

Abstract

The purpose of this paper is to introduce

α_{f}

-proximal

H

-contraction of the first and second kind in the setup of complete fuzzy metric space and to obtain optimal coincidence point results. The obtained results unify, extend and generalize various comparable [...] Read more.

The purpose of this paper is to introduce

α_{f}

-proximal

H

-contraction of the first and second kind in the setup of complete fuzzy metric space and to obtain optimal coincidence point results. The obtained results unify, extend and generalize various comparable results in the literature. We also present some examples to support the results obtained herein. Full article

(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)

14 pages, 280 KiB

Open AccessArticle

Fixed Point Results for α_*-ψ-Dominated Multivalued Contractive Mappings Endowed with Graphic Structure

by Tahair Rasham, Abdullah Shoaib, Badriah A. S. Alamri, Awais Asif and Muhammad Arshad

Mathematics 2019, 7(3), 307; https://doi.org/10.3390/math7030307 - 26 Mar 2019

Cited by 10 | Viewed by 2658

Abstract

The purpose of this paper is to establish fixed point results for a pair

α_{*}

-dominated multivalued mappings fulfilling generalized locally new

α_{*}

-

ψ

-Ćirić type rational contractive conditions on a closed ball in complete dislocated metric spaces. Examples and [...] Read more.

The purpose of this paper is to establish fixed point results for a pair

α_{*}

-dominated multivalued mappings fulfilling generalized locally new

α_{*}

-

ψ

-Ćirić type rational contractive conditions on a closed ball in complete dislocated metric spaces. Examples and applications are given to demonstrate the novelty of our results. Our results extend several comparable results in the existing literature. Full article

(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)

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