Special Issue "Mathematical Analysis and Analytic Number Theory 2019"

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

Deadline for manuscript submissions: 31 January 2020

Special Issue Editor

Guest Editor
Prof. Dr. Rekha Srivastava

Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
Website | E-Mail
Interests: mathematical analysis; applied mathematics; fractional calculus and its applications

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 wide-spread in many diverse areas of the mathematical, biological, physical, chemical, engineering, and statistical sciences. In this Special Issue, we invite and 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 many thanks in advance for your contributions.

Prof. Dr. Rekha 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 papers will be 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. Mathematics 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 850 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

  • 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 (4 papers)

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Research

Open AccessArticle
A Study of Third Hankel Determinant Problem for Certain Subfamilies of Analytic Functions Involving Cardioid Domain
Mathematics 2019, 7(5), 418; https://doi.org/10.3390/math7050418
Received: 18 April 2019 / Revised: 5 May 2019 / Accepted: 6 May 2019 / Published: 10 May 2019
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Abstract
In the present article, we consider certain subfamilies of analytic functions connected with the cardioid domain in the region of the unit disk. The purpose of this article is to investigate the estimates of the third Hankel determinant for these families. Further, the [...] Read more.
In the present article, we consider certain subfamilies of analytic functions connected with the cardioid domain in the region of the unit disk. The purpose of this article is to investigate the estimates of the third Hankel determinant for these families. Further, the same bounds have been investigated for two-fold and three-fold symmetric functions. Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2019)
Open AccessArticle
Remarks on the Generalized Fractional Laplacian Operator
Mathematics 2019, 7(4), 320; https://doi.org/10.3390/math7040320
Received: 25 February 2019 / Revised: 21 March 2019 / Accepted: 25 March 2019 / Published: 29 March 2019
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Abstract
The fractional Laplacian, also known as the Riesz fractional derivative operator, describes an unusual diffusion process due to random displacements executed by jumpers that are able to walk to neighbouring or nearby sites, as well as perform excursions to remote sites by way [...] Read more.
The fractional Laplacian, also known as the Riesz fractional derivative operator, describes an unusual diffusion process due to random displacements executed by jumpers that are able to walk to neighbouring or nearby sites, as well as perform excursions to remote sites by way of Lévy flights. The fractional Laplacian has many applications in the boundary behaviours of solutions to differential equations. The goal of this paper is to investigate the half-order Laplacian operator ( Δ ) 1 2 in the distributional sense, based on the generalized convolution and Temple’s delta sequence. Several interesting examples related to the fractional Laplacian operator of order 1 / 2 are presented with applications to differential equations, some of which cannot be obtained in the classical sense by the standard definition of the fractional Laplacian via Fourier transform. Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2019)
Open AccessArticle
On Geometric Properties of Normalized Hyper-Bessel Functions
Mathematics 2019, 7(4), 316; https://doi.org/10.3390/math7040316
Received: 18 February 2019 / Revised: 20 March 2019 / Accepted: 21 March 2019 / Published: 28 March 2019
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Abstract
In this paper, the normalized hyper-Bessel functions are studied. Certain sufficient conditions are determined such that the hyper-Bessel functions are close-to-convex, starlike and convex in the open unit disc. We also study the Hardy spaces of hyper-Bessel functions. Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2019)
Open AccessArticle
Some Reciprocal Classes of Close-to-Convex and Quasi-Convex Analytic Functions
Mathematics 2019, 7(4), 309; https://doi.org/10.3390/math7040309
Received: 18 December 2018 / Revised: 21 March 2019 / Accepted: 22 March 2019 / Published: 27 March 2019
PDF Full-text (247 KB) | HTML Full-text | XML Full-text
Abstract
The present paper comprises the study of certain functions which are analytic and defined in terms of reciprocal function. The reciprocal classes of close-to-convex functions and quasi-convex functions are defined and studied. Various interesting properties, such as sufficiency criteria, coefficient estimates, distortion results, [...] Read more.
The present paper comprises the study of certain functions which are analytic and defined in terms of reciprocal function. The reciprocal classes of close-to-convex functions and quasi-convex functions are defined and studied. Various interesting properties, such as sufficiency criteria, coefficient estimates, distortion results, and a few others, are investigated for these newly defined sub-classes. Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2019)
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