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

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 26753

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Special Issue Editor

Prof. Dr. Hari Mohan Srivastava

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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
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Special Issue Information

Dear Colleagues,

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

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. As in the abovementioned successful Special Issues, in this Special Issue, we invite and welcome review, expository and original research articles dealing with recent advances in mathematical analysis and its multidisciplinary applications.

We look forward to your contributions to this Special Issue.

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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Related Special Issues

Mathematical Analysis and Applications in Axioms (83 articles)
Mathematical Analysis and Applications II in Axioms (18 articles)
Mathematical Tools and Techniques Applicable to Probability Theory and Statistics in Axioms (13 articles)

Published Papers (14 papers)

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Research

14 pages, 314 KiB

Open AccessArticle

Ideals of Projections According to σ-Algebras and Unbounded Measurements

by Marjan Matvejchuk

Axioms 2023, 12(2), 167; https://doi.org/10.3390/axioms12020167 - 7 Feb 2023

Viewed by 1064

Abstract

A theory of unbounded measures is constructed based on the quantum logics of orthogonal projections. As an analogue of the ring of sets, the projector ideal is proposed. Finite and maximal measures regarding the projector ideals are described. Analogues of a number of classical theorems of measure theory are found. A wide class of unbounded measures on projection ideals is characterized. A number of sufficient conditions are found to extend unbounded measures to an integral of the entire algebra. The problem of describing unbounded

σ

-finite measures in semifinite algebras using von Neumann is similar to the Gleason problem. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications III)

10 pages, 790 KiB

Open AccessArticle

A Study of Monotonicity Analysis for the Delta and Nabla Discrete Fractional Operators of the Liouville–Caputo Family

by Pshtiwan Othman Mohammed, Christopher S. Goodrich, Hari Mohan Srivastava, Eman Al-Sarairah and Y. S. Hamed

Axioms 2023, 12(2), 114; https://doi.org/10.3390/axioms12020114 - 22 Jan 2023

Cited by 3 | Viewed by 1283

Abstract

In the present article, we explore the correlation between the sign of a Liouville–Caputo-type difference operator and the monotone behavior of the function upon which the difference operator acts. Finally, an example is also provided to demonstrate the application and the validation of [...] Read more.

(This article belongs to the Special Issue Mathematical Analysis and Applications III)

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14 pages, 827 KiB

Open AccessArticle

Coefficient Estimates of New Families of Analytic Functions Associated with q-Hermite Polynomials

by Isra Al-Shbeil, Adriana Cătaş, Hari Mohan Srivastava and Najla Aloraini

Axioms 2023, 12(1), 52; https://doi.org/10.3390/axioms12010052 - 3 Jan 2023

Cited by 15 | Viewed by 1570

Abstract

In this paper, we introduce two new subclasses of bi-univalent functions using the q-Hermite polynomials. Furthermore, we establish the bounds of the initial coefficients

υ_{2}

υ_{3}

, and

υ_{4}

of the Taylor–Maclaurin series and that of the Fekete–Szegö [...] Read more.

In this paper, we introduce two new subclasses of bi-univalent functions using the q-Hermite polynomials. Furthermore, we establish the bounds of the initial coefficients

υ_{2}

υ_{3}

, and

υ_{4}

of the Taylor–Maclaurin series and that of the Fekete–Szegö functional associated with the new classes, and we give the many consequences of our findings. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications III)

19 pages, 382 KiB

Open AccessArticle

Modified Padé–Borel Summation

by Simon Gluzman

Axioms 2023, 12(1), 50; https://doi.org/10.3390/axioms12010050 - 3 Jan 2023

Cited by 5 | Viewed by 2801

Abstract

We revisit the problem of calculating amplitude at infinity for the class of functions with power-law behavior at infinity by means of a resummation procedure based on the truncated series for small variables. Iterative Borel summation is applied by employing Padé approximants of the “odd” and “even” types modified to satisfy the power-law. The odd approximations are conventional and are asymptotically equivalent with an odd number of terms in the truncated series. Even approximants are new, and they are constructed based on the idea of corrected approximants. They are asymptotically equivalent to the even number of terms in truncated series. Odd- and even-modified Padé approximants could be applied with and without a Borel transformation. The four methods are applied to some basic examples from condensed matter physics. We found that modified Padé–Borel summation works well in the case of zero-dimensional field theory with fast-growing coefficients and for similar examples. Remarkably, the methodology of modified Padé–Borel summation appears to be extendible to the instances with slow decay or non-monotonous behavior. In such situations, exemplified by the problem of Bose condensation temperature shift, the results are still very good. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications III)

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10 pages, 1297 KiB

Open AccessArticle

On Classes of Non-Carathéodory Functions Associated with a Family of Functions Starlike in the Direction of the Real Axis

by Kadhavoor R. Karthikeyan, Nak Eun Cho and Gangadharan Murugusundaramoorthy

Axioms 2023, 12(1), 24; https://doi.org/10.3390/axioms12010024 - 25 Dec 2022

Cited by 4 | Viewed by 1405

Abstract

In this paper, we introduce a new class of analytic functions subordinated by functions which is not Carathéodory. We have obtained some interesting subordination properties, inclusion and integral representation of the defined function class. Several corollaries are presented to highlight the applications of [...] Read more.

(This article belongs to the Special Issue Mathematical Analysis and Applications III)

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7 pages, 305 KiB

Open AccessArticle

Classifying Topologies through

G

-Bases

by Juan Carlos Ferrando and Manuel López-Pellicer

Axioms 2022, 11(12), 744; https://doi.org/10.3390/axioms11120744 - 19 Dec 2022

Cited by 1 | Viewed by 1441

Abstract

We classify several topological properties of a Tychonoff space X by means of certain locally convex topologies

T

with a

G

-base located between the pointwise topology

τ_{p}

and the bounded-open topology

τ_{b}

of the real-valued continuous function space

C (X)

[...] Read more.

We classify several topological properties of a Tychonoff space X by means of certain locally convex topologies

T

with a

G

-base located between the pointwise topology

τ_{p}

and the bounded-open topology

τ_{b}

of the real-valued continuous function space

C (X)

. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications III)

11 pages, 288 KiB

Open AccessArticle

Criteria for Oscillation of Half-Linear Functional Differential Equations of Second-Order

by Barakah Almarri, Osama Moaaz and Ali Muhib

Axioms 2022, 11(12), 719; https://doi.org/10.3390/axioms11120719 - 12 Dec 2022

Cited by 2 | Viewed by 1465

Abstract

The present article aims to establish more effective criteria for testing the oscillation of a class of functional differential equations with delay arguments. In the non-canonical case, we deduce some improved monotonic and asymptotic properties of the class of decreasing positive solutions of the studied equation. Depending on both the new properties and the linear representation of the studied equation, we obtain new oscillation criteria. Moreover, we test the effectiveness of the new criteria by applying them to some special cases of the studied equation. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications III)

13 pages, 293 KiB

Open AccessArticle

Applications of the q-Derivative Operator to New Families of Bi-Univalent Functions Related to the Legendre Polynomials

by Ying Cheng, Rekha Srivastava and Jin-Lin Liu

Axioms 2022, 11(11), 595; https://doi.org/10.3390/axioms11110595 - 27 Oct 2022

Cited by 6 | Viewed by 1583

Abstract

By using the q-derivative operator and the Legendre polynomials, some new subclasses of q-starlike functions and bi-univalent functions are introduced. Several coefficient estimates and Fekete–Szegö-type inequalities for functions in each of these subclasses are obtained. The results derived in this article [...] Read more.

(This article belongs to the Special Issue Mathematical Analysis and Applications III)

10 pages, 10032 KiB

Open AccessArticle

The Laplace Transform of Composed Functions and Bivariate Bell Polynomials

by Diego Caratelli, Rekha Srivastava and Paolo Emilio Ricci

Axioms 2022, 11(11), 591; https://doi.org/10.3390/axioms11110591 - 26 Oct 2022

Cited by 2 | Viewed by 1378

Abstract

The problem of computing the Laplace transform of composed functions has not found its way into the literature because it was customarily believed that there were no suitable formula to solve it. Actually, it has been shown in previous work that by making use of Bell polynomials, efficient approximations can be found. Moreover, using an extension of Bell’s polynomials to bivariate functions, it is also possible to approximate the Laplace transform of composed functions of two variables. This topic is solved in this paper and some numerical verifications, due to the first author using the computer algebra system Mathematica

^{©}

, are given proving the effectiveness of the proposed method. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications III)

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13 pages, 309 KiB

Open AccessArticle

Geometric Properties of Some Generalized Mathieu Power Series inside the Unit Disk

by Živorad Tomovski, Stefan Gerhold, Deepak Bansal and Amit Soni

Axioms 2022, 11(10), 568; https://doi.org/10.3390/axioms11100568 - 19 Oct 2022

Cited by 1 | Viewed by 1519

Abstract

We consider two parametric families of special functions: One is defined by a power series generalizing the classical Mathieu series, and the other one is a generalized Mathieu type power series involving factorials in its coefficients. Using criteria due to Fejér and Ozaki, we provide sufficient conditions for these functions to be close-to-convex or starlike inside the unit disk, and thus univalent. One of our proofs is assisted by symbolic computation. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications III)

33 pages, 6960 KiB

Open AccessArticle

An Amended Whale Optimization Algorithm for Optimal Bidding in Day Ahead Electricity Market

by Kavita Jain, Akash Saxena, Ahmad M. Alshamrani, Adel Fahad Alrasheedi, Khalid Abdulaziz Alnowibet and Ali Wagdy Mohamed

Axioms 2022, 11(9), 456; https://doi.org/10.3390/axioms11090456 - 5 Sep 2022

Cited by 1 | Viewed by 2384

Abstract

Successful privatization in other sectors leads to a restructuring in the power sector. The same practice has been adopted in the electrical industry with a deregulated electricity market (EM). This enables competition among generating companies (Genco’s) for maximizing their profit and it plays a central role. With this aim, each Genco gives a higher bid that may result in a risk of losing the opportunity to get selected at auction. The big challenge in front of a Genco is to acquire an optimal bid and this process is known as the Optimal Bidding Strategy (OBS) of a Genco. In this manuscript, a new variant of whale optimization (WOA) termed the Amended Whale Optimization Algorithm (AWOA) is proposed, to attain the OBS of thermal Genco in an EM. Once the effectiveness of new AWOA is proved on 23 benchmark functions, it is applied to five Genco strategic bidding problems in a spot market with uniform price. The results obtained from the proposed AWOA are compared with other competitive algorithms. The results reflect that AWOA outperforms in terms of the profit and convergence rate. Simulations also indicate that the proposed AWOA can successfully be used for an OBS in the EM. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications III)

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17 pages, 321 KiB

Open AccessArticle

A Fuzzy Random Boundary Value Problem

by Hari M. Srivastava, Reza Chaharpashlou, Reza Saadati and Chenkuan Li

Axioms 2022, 11(8), 414; https://doi.org/10.3390/axioms11080414 - 18 Aug 2022

Cited by 1 | Viewed by 1387

Abstract

A system of generalized fuzzy random differential equations with boundary conditions is investigated, which is a fuzzy version of a system of general random differential equations. We first present random fixed point (RFP) theorems in fuzzy metric space (FM). In the sequel, we define the operators that are of integral type. Furthermore, these operators are related to a part of random differential equations (RDE). For the desired system with boundary conditions, we study the suitable integral operators associated with a large family of random differential equations. Finally, we prove the existence of a unique random solution (EURS). Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications III)

21 pages, 354 KiB

Open AccessFeature PaperArticle

Optimal Mittag–Leffler Summation

by Simon Gluzman

Axioms 2022, 11(5), 202; https://doi.org/10.3390/axioms11050202 - 24 Apr 2022

Cited by 6 | Viewed by 3517

Abstract

A novel method of an optimal summation is developed that allows for calculating from small-variable asymptotic expansions the characteristic amplitudes for variables tending to infinity. The method is developed in two versions, as the self-similar Borel–Leroy or Mittag–Leffler summations. It is based on optimized self-similar iterated roots approximants applied to the Borel–Leroy and Mittag–Leffler- transformed series with the subsequent inverse transformations. As a result, simple and transparent expressions for the critical amplitudes are obtained in explicit form. The control parameters come into play from the Borel–Leroy and Mittag–Leffler transformations. They are determined from the optimization procedure, either from the minimal derivative or minimal difference conditions, imposed on the analytically expressed critical amplitudes. After diff-log transformation, virtually the same procedure can be applied to critical indices at infinity. The results are obtained for a number of various examples. The examples vary from a rapid growth of the coefficients to a fast decay, as well as intermediate cases. The methods give good estimates for the large-variable critical amplitudes and exponents. The Mittag–Leffler summation works uniformly well for a wider variety of examples. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications III)

14 pages, 1011 KiB

Open AccessArticle

An Effective Approximation Algorithm for Second-Order Singular Functional Differential Equations

by Mohammad Izadi, Hari M. Srivastava and Waleed Adel

Axioms 2022, 11(3), 133; https://doi.org/10.3390/axioms11030133 - 14 Mar 2022

Cited by 11 | Viewed by 2364

Abstract

In this research study, a novel computational algorithm for solving a second-order singular functional differential equation as a generalization of the well-known Lane–Emden and differential-difference equations is presented by using the Bessel bases. This technique depends on transforming the problem into a system of algebraic equations and by solving this system the unknown Bessel coefficients are determined and the solution will be known. The method is tested on several test examples and proves to provide accurate results as compared to other existing methods from the literature. The simplicity and robustness of the proposed technique drive us to investigate more of their applications to several similar problems in the future. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications III)

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