Special Issue "Mathematical Analysis and Analytic Number Theory 2020"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 30 June 2021.

Special Issue Editor

Prof. Dr. Rekha Srivastava
E-Mail Website
Guest Editor
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
Interests: mathematical analysis; applied mathematics; fractional calculus and its applications
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

Investigations involving the theory and applications of the various tools and techniques of mathematical analysis and analytic number theory are remarkably widespread in many diverse areas of the mathematical, biological, physical, chemical, engineering, and statistical sciences. In this Special Issue, we welcome original as well as review-cum-expository research articles dealing with recent and new developments on the topics of mathematical analysis and analytic number theory as well as their multidisciplinary applications.

We look forward to receiving and editorially processing your contributions to this Special Issue.

With kind regards and thanks in advance for your contributions.

Prof. Dr. Rekha Srivastava
Guest Editor

Manuscript Submission Information

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Keywords

  • Theory and applications of the tools and techniques of mathematical analysis
  • Theory and applications of the tools and techniques of analytic number theory
  • Applications involving special (or higher transcendental) functions
  • Applications involving fractional-order differential and differintegral equations
  • Applications involving q-Series and q-Polynomials
  • Applications involving special functions of mathematical physics and applied mathematics
  • Applications involving geometric function theory of complex analysis
  • Applications involving real analysis and operator theory

Published Papers (11 papers)

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Research

Open AccessArticle
Repdigits as Product of Terms of k-Bonacci Sequences
Mathematics 2021, 9(6), 682; https://doi.org/10.3390/math9060682 - 22 Mar 2021
Viewed by 313
Abstract
For any integer k2, the sequence of the k-generalized Fibonacci numbers (or k-bonacci numbers) is defined by the k initial values F(k2)(k)==F0(k)=0 and F1(k)=1 and such that each term afterwards is the sum of the k preceding ones. In this paper, we search for repdigits (i.e., a number whose decimal expansion is of the form aaa, with a[1,9]) in the sequence (Fn(k)Fn(k+m))n, for m[1,9]. This result generalizes a recent work of Bednařík and Trojovská (the case in which (k,m)=(2,1)). Our main tools are the transcendental method (for Diophantine equations) together with the theory of continued fractions (reduction method). Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2020)
Open AccessArticle
On Four Classical Measure Theorems
Mathematics 2021, 9(5), 526; https://doi.org/10.3390/math9050526 - 03 Mar 2021
Viewed by 279
Abstract
A subset B of an algebra A of subsets of a set Ω has property (N) if each B-pointwise bounded sequence of the Banach space ba(A) is bounded in ba(A), where ba(A) is the Banach space of real or complex bounded finitely additive measures defined on A endowed with the variation norm. B has property (G) [(VHS)] if for each bounded sequence [if for each sequence] in ba(A) the B-pointwise convergence implies its weak convergence. B has property (sN) [(sG) or (sVHS)] if every increasing covering {Bn:nN} of B contains a set Bp with property (N) [(G) or (VHS)], and B has property (wN) [(wG) or (wVHS)] if every increasing web {Bn1n2nm:niN,1im,mN} of B contains a strand {Bp1p2pm:mN} formed by elements Bp1p2pm with property (N) [(G) or (VHS)] for every mN. The classical theorems of Nikodým–Grothendieck, Valdivia, Grothendieck and Vitali–Hahn–Saks say, respectively, that every σ-algebra has properties (N), (sN), (G) and (VHS). Valdivia’s theorem was obtained through theorems of barrelled spaces. Recently, it has been proved that every σ-algebra has property (wN) and several applications of this strong Nikodým type property have been provided. In this survey paper we obtain a proof of the property (wN) of a σ-algebra independent of the theory of locally convex barrelled spaces which depends on elementary basic results of Measure theory and Banach space theory. Moreover we prove that a subset B of an algebra A has property (wWHS) if and only if B has property (wN) and A has property (G). Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2020)
Open AccessFeature PaperArticle
On Coding by (2,q)-Distance Fibonacci Numbers
Mathematics 2020, 8(11), 2058; https://doi.org/10.3390/math8112058 - 18 Nov 2020
Viewed by 448
Abstract
In 2006, A. Stakhov introduced a new coding/decoding process based on generating matrices of the Fibonacci p-numbers, which he called the Fibonacci coding/decoding method. Stakhov’s papers have motivated many other scientists to seek certain generalizations by introducing new additional coefficients into recurrence [...] Read more.
In 2006, A. Stakhov introduced a new coding/decoding process based on generating matrices of the Fibonacci p-numbers, which he called the Fibonacci coding/decoding method. Stakhov’s papers have motivated many other scientists to seek certain generalizations by introducing new additional coefficients into recurrence of Fibonacci p-numbers. In 2013, I. Włoch et al. studied (2,q)-distance Fibonacci numbers F2(q,n) and found some of their combinatorial properties. In this paper, we state a new coding theory based on the sequence (Tq(n))n=, which is an extension of Włoch’s sequence (F2(q,n))n=0. Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2020)
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Open AccessArticle
A New Representation of the Generalized Krätzel Function
Mathematics 2020, 8(11), 2009; https://doi.org/10.3390/math8112009 - 11 Nov 2020
Viewed by 462
Abstract
The confluence of distributions (generalized functions) with integral transforms has become a remarkably powerful tool to address important unsolved problems. The purpose of the present study is to investigate a distributional representation of the generalized Krätzel function. Hence, a new definition of these [...] Read more.
The confluence of distributions (generalized functions) with integral transforms has become a remarkably powerful tool to address important unsolved problems. The purpose of the present study is to investigate a distributional representation of the generalized Krätzel function. Hence, a new definition of these functions is formulated over a particular set of test functions. This is validated using the classical Fourier transform. The results lead to a novel extension of Krätzel functions by introducing distributions in terms of the delta function. A new version of the generalized Krätzel integral transform emerges as a natural consequence of this research. The relationship between the Krätzel function and the H-function is also explored to study new identities. Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2020)
Open AccessArticle
An Alternating Sum of Fibonacci and Lucas Numbers of Order k
Mathematics 2020, 8(9), 1487; https://doi.org/10.3390/math8091487 - 03 Sep 2020
Cited by 2 | Viewed by 673
Abstract
During the last decade, many researchers have focused on proving identities that reveal the relation between Fibonacci and Lucas numbers. Very recently, one of these identities has been generalized to the case of Fibonacci and Lucas numbers of order k. In the [...] Read more.
During the last decade, many researchers have focused on proving identities that reveal the relation between Fibonacci and Lucas numbers. Very recently, one of these identities has been generalized to the case of Fibonacci and Lucas numbers of order k. In the present work, we state and prove a new identity regarding an alternating sum of Fibonacci and Lucas numbers of order k. Our result generalizes recent works in this direction. Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2020)
Open AccessArticle
On the Quartic Residues and Their New Distribution Properties
Mathematics 2020, 8(8), 1337; https://doi.org/10.3390/math8081337 - 11 Aug 2020
Cited by 1 | Viewed by 423
Abstract
In this paper, we use the analytic methods, the properties of the fourth-order characters, and the estimate for character sums to study the computational problems of one kind of special quartic residues modulo p, and give an exact calculation formula and asymptotic [...] Read more.
In this paper, we use the analytic methods, the properties of the fourth-order characters, and the estimate for character sums to study the computational problems of one kind of special quartic residues modulo p, and give an exact calculation formula and asymptotic formula for their counting functions. Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2020)
Open AccessArticle
On the Generalized Riesz Derivative
Mathematics 2020, 8(7), 1089; https://doi.org/10.3390/math8071089 - 03 Jul 2020
Viewed by 682
Abstract
The goal of this paper is to construct an integral representation for the generalized Riesz derivative R Z D x 2 s u ( x ) for k < s < k + 1 with k = 0 , 1 , , which is proved to be a one-to-one and linearly continuous mapping from the normed space W k + 1 ( R ) to the Banach space C ( R ) . In addition, we show that R Z D x 2 s u ( x ) is continuous at the end points and well defined for s = 1 2 + k . Furthermore, we extend the generalized Riesz derivative R Z D x 2 s u ( x ) to the space C k ( R n ) , where k is an n-tuple of nonnegative integers, based on the normalization of distribution and surface integrals over the unit sphere. Finally, several examples are presented to demonstrate computations for obtaining the generalized Riesz derivatives. Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2020)
Open AccessArticle
A Study of the Second-Kind Multivariate Pseudo-Chebyshev Functions of Fractional Degree
Mathematics 2020, 8(6), 978; https://doi.org/10.3390/math8060978 - 16 Jun 2020
Cited by 2 | Viewed by 464
Abstract
Here, in this paper, the second-kind multivariate pseudo-Chebyshev functions of fractional degree are introduced by using the Dunford–Taylor integral. As an application, the problem of finding matrix roots for a wide class of non-singular complex matrices has been considered. The principal value of [...] Read more.
Here, in this paper, the second-kind multivariate pseudo-Chebyshev functions of fractional degree are introduced by using the Dunford–Taylor integral. As an application, the problem of finding matrix roots for a wide class of non-singular complex matrices has been considered. The principal value of the fixed matrix root is determined. In general, by changing the determinations of the numerical roots involved, we could find n r roots for the n-th root of an r × r matrix. The exceptional cases for which there are infinitely many roots, or no roots at all, are obviously excluded. Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2020)
Open AccessArticle
Better Approaches for n-Times Differentiable Convex Functions
Mathematics 2020, 8(6), 950; https://doi.org/10.3390/math8060950 - 10 Jun 2020
Cited by 16 | Viewed by 581
Abstract
In this work, by using an integral identity together with the Hölder–İşcan inequality we establish several new inequalities for n-times differentiable convex and concave mappings. Furthermore, various applications for some special means as arithmetic, geometric, and logarithmic are given. Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2020)
Open AccessArticle
A Certain Mean Square Value Involving Dirichlet L-Functions
Mathematics 2020, 8(6), 948; https://doi.org/10.3390/math8060948 - 09 Jun 2020
Viewed by 491
Abstract
The main purpose of this article is using the elementary methods, the properties of Dirichlet L-functions to study the computational problem of a certain mean square value involving Dirichlet L-functions at positive integer points, and give some exact calculating formulae. As [...] Read more.
The main purpose of this article is using the elementary methods, the properties of Dirichlet L-functions to study the computational problem of a certain mean square value involving Dirichlet L-functions at positive integer points, and give some exact calculating formulae. As some applications, we obtain some interesting identities and inequalities involving character sums and trigonometric sums. Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2020)
Open AccessArticle
Fekete-Szegö Type Problems and Their Applications for a Subclass of q-Starlike Functions with Respect to Symmetrical Points
Mathematics 2020, 8(5), 842; https://doi.org/10.3390/math8050842 - 22 May 2020
Cited by 5 | Viewed by 644
Abstract
In this article, by using the concept of the quantum (or q-) calculus and a general conic domain Ω k , q , we study a new subclass of normalized analytic functions with respect to symmetrical points in an open unit disk. We solve the Fekete-Szegö type problems for this newly-defined subclass of analytic functions. We also discuss some applications of the main results by using a q-Bernardi integral operator. Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2020)
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