A Themed Issue on Mathematical Inequalities, Analytic Combinatorics and Related Topics in Honor of Professor Feng Qi

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

Deadline for manuscript submissions: closed (30 April 2023) | Viewed by 19931

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Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
Interests: nonlinear analysis and its applications; fixed point theory; variational principles and inequalities; optimization theory; equilibrium problems; fractional calculus theory
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1. ETSI Division of Applied Mathematics, Thu Dau Mot University, Thủ Dầu Một, Binh Duong, Vietnam
2. Department of Mathematics, Çankaya University, 06790, Etimesgut, Ankara, Turkey
3. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
Interests: functional analysis; operator theory; linear topological invariants; fixed point theory; best proximity

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Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia
Interests: abstract Volterra integro-differential equations; abstract fractional differential equations; topological dynamics of linear operators and abstract PDEs
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School of Mathematics, Hangzhou Normal University, Hangzhou 311121, Zhejiang, China
Interests: mathematical inequalities and means; analytic combinatorics; q-series; q-difference equations; generating functions; fractional q-calculus
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Special Issue Information

Dear Colleagues,

Professor Feng Qi received his Ph.D. degree from the University of Science and Technology of China in 1999 and is currently a full Professor at Tiangong University and Henan Polytechnic University, China. He was invited to visit Victoria University in Australia and the University of Hong Kong twice for academic collaborations, and he was invited to visit the University of Copenhagen, Denmark; Antalya Bilim University in Turkey; several universities in South Korea; Sun Yat-sen University, China; and Kaohsiung Normal University, China for conferences, special lectures, or other academic activities. He is or was the editor-in-chief, an associate editor, or a member of the editorial board of about 40 reputable international journals. Since 1993, he has published over 660 papers in 215 journals, collections, or proceedings. He took charge of and participated in two national research projects supported by the National Natural Science Foundation of China and several provincial scientific projects supported by Henan Province in China. Since 1992, he has acquired about one and a half millions CNY of funding support. In Stanford University’s 2021 list of World’s Top 2% Scientists, among 190,064 scientists in the Single Year Impact Data (2020), he ranked 61,510 and, among 186,178 scientists in the Career-long Data (1960–2020), he ranked 96,040. In the 2022 edition of the World's Top Mathematics Scientists by Research.com, he currently ranks 329. Currently, his academic interests and research fields mainly include the theory of special functions, classical analysis, mathematical inequalities and applications, mathematical means and applications, analytic combinatorics, analytic number theory, etc. 

The purpose of this Special Issue is to pay tribute to the significant contributions made by Professor Feng Qi in these fields and to provide some important recent advances in theory, methods, and applications. We cordially and earnestly invite researchers to contribute their original and high-quality research papers, which will inspire more advances in mathematical inequalities, number theory, combinatorics, nonlinear analysis, optimization, and their applications. Potential topics include but are not limited to the following:

  • Mathematical inequalities and applications;
  • Mathematical means and applications;
  • The theory of special functions;
  • Analytic combinatorics;
  • Analytic number theory;
  • Nonlinear functional analysis;
  • Optimization;
  • Convex analysis of functions;
  • Matrix theory.

Prof. Dr. Wei-Shih Du
Prof. Dr. Ravi P. Agarwal
Prof. Dr. Erdal Karapinar
Prof. Dr. Marko Kostić
Prof. Dr. Jian Cao
Guest Editors

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 inequalities and means
  • special functions
  • analytic combinatorics
  • analytic number theory
  • nonlinear functional analysis
  • classical analysis
  • optimization
  • convex analysis
  • matrix theory

Published Papers (13 papers)

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Editorial

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5 pages, 943 KiB  
Editorial
Preface to the Special Issue “A Themed Issue on Mathematical Inequalities, Analytic Combinatorics and Related Topics in Honor of Professor Feng Qi”
by Wei-Shih Du, Ravi Prakash Agarwal, Erdal Karapinar, Marko Kostić and Jian Cao
Axioms 2023, 12(9), 846; https://doi.org/10.3390/axioms12090846 - 30 Aug 2023
Cited by 1 | Viewed by 860
Abstract
This Special Issue of the journal Axioms pays tribute to Professor Feng Qi’s significant contributions and provides some important recent advances in mathematics [...] Full article
27 pages, 20727 KiB  
Editorial
A Brief Overview and Survey of the Scientific Work by Feng Qi
by Ravi Prakash Agarwal, Erdal Karapinar, Marko Kostić, Jian Cao and Wei-Shih Du
Axioms 2022, 11(8), 385; https://doi.org/10.3390/axioms11080385 - 05 Aug 2022
Cited by 4 | Viewed by 1819
Abstract
In the paper, the authors present a brief overview and survey of the scientific work by Chinese mathematician Feng Qi and his coauthors. Full article
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Research

Jump to: Editorial

11 pages, 263 KiB  
Article
Some New Estimates of Hermite–Hadamard Inequality with Application
by Tao Zhang and Alatancang Chen
Axioms 2023, 12(7), 688; https://doi.org/10.3390/axioms12070688 - 14 Jul 2023
Viewed by 545
Abstract
This paper establishes several new inequalities of Hermite–Hadamard type for |f|q being convex for some fixed q(0,1]. As application, some error estimates on special means of real numbers are given. Full article
10 pages, 258 KiB  
Article
Inequalities for the Windowed Linear Canonical Transform of Complex Functions
by Zhen-Wei Li and Wen-Biao Gao
Axioms 2023, 12(6), 554; https://doi.org/10.3390/axioms12060554 - 04 Jun 2023
Viewed by 836
Abstract
In this paper, we generalize the N-dimensional Heisenberg’s inequalities for the windowed linear canonical transform (WLCT) of a complex function. Firstly, the definition for N-dimensional WLCT of a complex function is given. In addition, the N-dimensional Heisenberg’s inequality for the linear canonical transform [...] Read more.
In this paper, we generalize the N-dimensional Heisenberg’s inequalities for the windowed linear canonical transform (WLCT) of a complex function. Firstly, the definition for N-dimensional WLCT of a complex function is given. In addition, the N-dimensional Heisenberg’s inequality for the linear canonical transform (LCT) is derived. It shows that the lower bound is related to the covariance and can be achieved by a complex chirp function with a Gaussian function. Finally, the N-dimensional Heisenberg’s inequality for the WLCT is exploited. In special cases, its corollary can be obtained. Full article
22 pages, 339 KiB  
Article
Self-Improving Properties of Continuous and Discrete Muckenhoupt Weights: A Unified Approach
by Maryam M. Abuelwafa, Ravi P. Agarwal, Safi S. Rabie and Samir H. Saker
Axioms 2023, 12(6), 505; https://doi.org/10.3390/axioms12060505 - 23 May 2023
Viewed by 756
Abstract
In this paper, we develop a new technique on a time scale T to prove that the self-improving properties of the Muckenhoupt weights hold. The results contain the properties of the weights when T=R and when T=N, and [...] Read more.
In this paper, we develop a new technique on a time scale T to prove that the self-improving properties of the Muckenhoupt weights hold. The results contain the properties of the weights when T=R and when T=N, and also can be extended to cover different spaces such as T=hN, T=qN, etc. The results will be proved by employing some new refinements of Hardy’s type dynamic inequalities with negative powers proven and designed for this purpose. The results give the exact value of the limit exponent as well as the new constants of the new classes. Full article
13 pages, 424 KiB  
Article
Reinsurance Policy under Interest Force and Bankruptcy Prohibition
by Yangmin Zhong and Huaping Huang
Axioms 2023, 12(4), 378; https://doi.org/10.3390/axioms12040378 - 16 Apr 2023
Viewed by 1217
Abstract
In this paper, we solve an optimal reinsurance problem in the mathematical finance area. We assume that the surplus process of the insurance company follows a controlled diffusion process and the constant interest rate is involved in the financial model. During the whole [...] Read more.
In this paper, we solve an optimal reinsurance problem in the mathematical finance area. We assume that the surplus process of the insurance company follows a controlled diffusion process and the constant interest rate is involved in the financial model. During the whole optimization period, the company has a choice to buy reinsurance contract and decide the reinsurance retention level. Meanwhile, the bankruptcy at the terminal time is not allowed. The aim of the optimization problem is to minimize the distance between the terminal wealth and a given goal by controlling the reinsurance proportion. Using the stochastic control theory, we derive the Hamilton-Jacobi-Bellman equation for the optimization problem. Via adopting the technique of changing variable as well as the dual transformation, an explicit solution of the value function and the optimal policy are shown. Finally, several numerical examples are shown, from which we find several main factors that affect the optimal reinsurance policy. Full article
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20 pages, 333 KiB  
Article
Inequalities and Reverse Inequalities for the Joint A-Numerical Radius of Operators
by Najla Altwaijry, Silvestru Sever Dragomir and Kais Feki
Axioms 2023, 12(3), 316; https://doi.org/10.3390/axioms12030316 - 22 Mar 2023
Viewed by 1063
Abstract
In this paper, we aim to establish several estimates concerning the generalized Euclidean operator radius of d-tuples of A-bounded linear operators acting on a complex Hilbert space H, which leads to the special case of the well-known A-numerical radius [...] Read more.
In this paper, we aim to establish several estimates concerning the generalized Euclidean operator radius of d-tuples of A-bounded linear operators acting on a complex Hilbert space H, which leads to the special case of the well-known A-numerical radius for d=1. Here, A is a positive operator on H. Some inequalities related to the Euclidean operator A-seminorm of d-tuples of A-bounded operators are proved. In addition, under appropriate conditions, several reverse bounds for the A-numerical radius in single and multivariable settings are also stated. Full article
8 pages, 250 KiB  
Article
Schur-Convexity of the Mean of Convex Functions for Two Variables
by Huan-Nan Shi, Dong-Sheng Wang and Chun-Ru Fu
Axioms 2022, 11(12), 681; https://doi.org/10.3390/axioms11120681 - 29 Nov 2022
Cited by 1 | Viewed by 1111
Abstract
The results of Schur convexity established by Elezovic and Pecaric for the average of convex functions are generalized relative to the case of the means for two-variable convex functions. As an application, some binary mean inequalities are given. Full article
12 pages, 304 KiB  
Article
Hermite–Hadamard’s Integral Inequalities of (α, s)-GA- and (α, s, m)-GA-Convex Functions
by Jing-Yu Wang, Hong-Ping Yin, Wen-Long Sun and Bai-Ni Guo
Axioms 2022, 11(11), 616; https://doi.org/10.3390/axioms11110616 - 06 Nov 2022
Cited by 2 | Viewed by 1059
Abstract
In this paper, the authors propose the notions of (α,s)-geometric-arithmetically convex functions and (α,s,m)-geometric-arithmetically convex functions, while they establish some new integral inequalities of the Hermite–Hadamard type for [...] Read more.
In this paper, the authors propose the notions of (α,s)-geometric-arithmetically convex functions and (α,s,m)-geometric-arithmetically convex functions, while they establish some new integral inequalities of the Hermite–Hadamard type for (α,s)-geometric-arithmetically convex functions and for (α,s,m)-geometric-arithmetically convex functions. Full article
12 pages, 281 KiB  
Article
Several Double Inequalities for Integer Powers of the Sinc and Sinhc Functions with Applications to the Neuman–Sándor Mean and the First Seiffert Mean
by Wen-Hui Li, Qi-Xia Shen and Bai-Ni Guo
Axioms 2022, 11(7), 304; https://doi.org/10.3390/axioms11070304 - 23 Jun 2022
Cited by 3 | Viewed by 2470
Abstract
In the paper, the authors establish a general inequality for the hyperbolic functions, extend the newly-established inequality to trigonometric functions, obtain some new inequalities involving the inverse sine and inverse hyperbolic sine functions, and apply these inequalities to the Neuman–Sándor mean and the [...] Read more.
In the paper, the authors establish a general inequality for the hyperbolic functions, extend the newly-established inequality to trigonometric functions, obtain some new inequalities involving the inverse sine and inverse hyperbolic sine functions, and apply these inequalities to the Neuman–Sándor mean and the first Seiffert mean. Full article
10 pages, 260 KiB  
Article
Context-Free Grammars for Several Triangular Arrays
by Roberta Rui Zhou, Jean Yeh and Fuquan Ren
Axioms 2022, 11(6), 297; https://doi.org/10.3390/axioms11060297 - 20 Jun 2022
Viewed by 1363
Abstract
In this paper, we present a unified grammatical interpretation of the numbers that satisfy a kind of four-term recurrence relation, including the Bell triangle, the coefficients of modified Hermite polynomials, and the Bessel polynomials. Additionally, as an application, a criterion for real zeros [...] Read more.
In this paper, we present a unified grammatical interpretation of the numbers that satisfy a kind of four-term recurrence relation, including the Bell triangle, the coefficients of modified Hermite polynomials, and the Bessel polynomials. Additionally, as an application, a criterion for real zeros of row-generating polynomials is also presented. Full article
8 pages, 245 KiB  
Article
New Inequalities and Generalizations for Symmetric Means Induced by Majorization Theory
by Huan-Nan Shi and Wei-Shih Du
Axioms 2022, 11(6), 279; https://doi.org/10.3390/axioms11060279 - 09 Jun 2022
Viewed by 1553
Abstract
In this paper, the authors study new inequalities and generalizations for symmetric means and give new proofs for some known results by applying majorization theory. Full article
12 pages, 285 KiB  
Article
Bounds for the Neuman–Sándor Mean in Terms of the Arithmetic and Contra-Harmonic Means
by Wen-Hui Li, Peng Miao and Bai-Ni Guo
Axioms 2022, 11(5), 236; https://doi.org/10.3390/axioms11050236 - 19 May 2022
Cited by 4 | Viewed by 1732
Abstract
In this paper, the authors provide several sharp upper and lower bounds for the Neuman–Sándor mean in terms of the arithmetic and contra-harmonic means, and present some new sharp inequalities involving hyperbolic sine function and hyperbolic cosine function. Full article
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