OMA – Vol 8 – Issue 1 (2024) – PISRT https://old.pisrt.org Fri, 26 Jul 2024 04:04:03 +0000 en-US hourly 1 https://wordpress.org/?v=6.7 A direct proof of stability of nonnegative weak solution for fractional \(\mathbf{p}\)-Laplacian problem with concave nonlinearity https://old.pisrt.org/psr-press/journals/oma-vol-8-issue-1-2024/a-direct-proof-of-stability-of-nonnegative-weak-solution-for-fractional-mathbfp-laplacian-problem-with-concave-nonlinearity/ Sat, 06 Jul 2024 15:03:18 +0000 https://old.pisrt.org/?p=8373
OMA-Vol. 8 (2024), Issue 1, pp. 76 - 79 Open Access Full-Text PDF
Salah A. Khafagy
Abstract: The present paper provides a direct proof of stability of nontrivial nonnegative weak solution for fractional \(p\)-Laplacian problem under concave nonlinearity condition. The main results of this work are extend the previously known results for the fractional Laplacian problem. ]]>
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Open Journal of Mathematical Analysis
Vol. 8 (2024), Issue 1, pp. 76 – 79
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2024.0136

A direct proof of stability of nonnegative weak solution for fractional \(\mathbf{p}\)-Laplacian problem with concave nonlinearity

Salah A. Khafagy\(^{1,*}\)
\(^{1}\) Department of Mathematics, Royal University of Phnom Penh, Phnom Penh, Cambodia.

Copyright © 2024 Salah A. Khafagy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: April 20, 2024 – Accepted: May 8, 2024 – Published: June 30, 2024

Abstract

The present paper provides a direct proof of stability of nontrivial nonnegative weak solution for fractional \(p\)-Laplacian problem under concave nonlinearity condition. The main results of this work are extend the previously known results for the fractional Laplacian problem.

Keywords:

Stability; weak solution; fractional \(p\)-Laplacian
]]> Contributions to hyperbolic 1-parameter inequalities https://old.pisrt.org/psr-press/journals/oma-vol-8-issue-1-2024/contributions-to-hyperbolic-1-parameter-inequalities/ Sat, 06 Jul 2024 13:48:59 +0000 https://old.pisrt.org/?p=8369
OMA-Vol. 8 (2024), Issue 1, pp. 57–75 Open Access Full-Text PDF
Abd Raouf Chouikha and Christophe Chesneau
Abstract:In this article we provide classes of hyperbolic chains of inequalities depending on a certain parameter \(n\). New refinements as well as new results are offered. Some graphical analyses support the theoretical results. ]]>
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Open Journal of Mathematical Analysis
Vol. 8 (2024), Issue 1, pp. 57 – 75
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2024.0135

Contributions to hyperbolic 1-parameter inequalities

Abd Raouf Chouikha\(^{1,*}\) and Christophe Chesneau\(^{2}\)
\(^{1}\) Universite Paris-Sorbonne, Paris-Nord, Institut Galilee, LAGA, 93400 Villetaneuse, France
\(^{2}\) Department of Mathematics, LMNO, University of Caen, 14032 Caen, France

Copyright © 2024 Abd Raouf Chouikha and Christophe Chesneau. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: April 21, 2024 – Accepted: June 28, 2024 – Published: June 30, 2024

Abstract

In this article we provide classes of hyperbolic chains of inequalities depending on a certain parameter \(n\). New refinements as well as new results are offered. Some graphical analyses support the theoretical results.

Keywords:

hyperbolic functions; sinc function; hyperbolic inequalities; inequality chains
]]> On Schur power convexity of generalized invariant contra harmonic means with respect to geometric means https://old.pisrt.org/psr-press/journals/oma-vol-8-issue-1-2024/on-schur-power-convexity-of-generalized-invariant-contra-harmonic-means-with-respect-to-geometric-means/ Sat, 06 Jul 2024 13:36:34 +0000 https://old.pisrt.org/?p=8365
OMA-Vol. 8 (2024), Issue 1, pp. 45 – 56 Open Access Full-Text PDF
Huan-Nan Shi, Fei Wang, Jing Zhang and Wei-Shih Du
Abstract:In this article, we investigate the power convexity of two generalized forms of the invariant of the contra harmonic mean with respect to the geometric mean, and establish several inequalities involving bivariate power mean as applications. Some open problems related to the Schur power convexity and concavity are also given. ]]>
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Open Journal of Mathematical Analysis
Vol. 8 (2024), Issue 1, pp. 45 – 56
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2024.0134

On Schur power convexity of generalized invariant contra harmonic means with respect to geometric means

Huan-Nan Shi\(^{1}\), Fei Wang\(^{2}\), Jing Zhang\(^{3}\) and Wei-Shih Du\(^{4,*}\)
\(^{1}\) Department of Electronic Information, Teacher’s College, Beijing Union University, Beijing City, 100011, China
\(^{2}\) Mathematics Teaching and Research Section, Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou, Zhejiang, 310053, China
\(^{3}\) Institute of Fundamental and Interdisciplinary Sciences, Beijing Union University, Beijing 100101, China
\(^{4}\) Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan

Copyright © 2024 Huan-Nan Shi, Fei Wang, Jing Zhang and Wei-Shih Du. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: April 30, 2024 – Accepted: June 28, 2024 – Published: June 30, 2024

Abstract

In this article, we investigate the power convexity of two generalized forms of the invariant of the contra harmonic mean with respect to the geometric mean, and establish several inequalities involving bivariate power mean as applications. Some open problems related to the Schur power convexity and concavity are also given.

Keywords:

Schur power convexity; generalized invariant contra harmonic mean; majorization; binary power mean.
]]> Multidual Gamma function https://old.pisrt.org/psr-press/journals/oma-vol-8-issue-1-2024/multidual-gamma-function/ Sat, 06 Jul 2024 13:19:22 +0000 https://old.pisrt.org/?p=8363
OMA-Vol. 8 (2024), Issue 1, pp. 36 – 44 Open Access Full-Text PDF
Farid Messelmi
Abstract: The purpose of this paper is to contribute to the development of the multidual Gamma function. For this aim, we start by defining the multidual Gamma and we propose a multidual analysis technics of in order to show a result regarding real Gamma function. ]]>
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Open Journal of Mathematical Analysis
Vol. 8 (2024), Issue 1, pp. 36 – 44
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2024.0133

Multidual Gamma function

Farid Messelmi\(^{1,*}\)
\(^{1}\) Department of Mathematics and LDMM Laboratory, University of Djelfa, Algeria.

Copyright © 2024 Farid Messelmi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: April 30, 2024 – Accepted: June 28, 2024 – Published: June 30, 2024

Abstract

The purpose of this paper is to contribute to the development of the multidual Gamma function. For this aim, we start by defining the multidual Gamma and we propose a multidual analysis technics of in order to show a result regarding real Gamma function.

Keywords:

Multidual Gamma function; extention
]]> Convergence analysis of tunable product sequences and series with two tuning parameters and two functions https://old.pisrt.org/psr-press/journals/oma-vol-8-issue-1-2024/convergence-analysis-of-tunable-product-sequences-and-series-with-two-tuning-parameters-and-two-functions/ Sat, 06 Jul 2024 13:14:05 +0000 https://old.pisrt.org/?p=8361
OMA-Vol. 8 (2024), Issue 1, pp. 18–35 Open Access Full-Text PDF
Christophe Chesneau
Abstract:The study of innovative sequences and series is important in several fields. In this article, we examine the convergence properties of a particular product series that offers adaptability through two parameters and two functions. Based on this analysis, we extend our investigation to a related series. Our main theorems are proved in detail and include several new intermediate results that can be used for other convergence analysis purposes. This is particularly the case for a generalized version of the Riemann sum formula. Several precise examples are presented and discussed, including one related to the gamma function.]]>
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Open Journal of Mathematical Analysis
Vol. 8 (2024), Issue 1, pp. 18 – 35
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2024.0132

Convergence analysis of tunable product sequences and series with two tuning parameters and two functions

Christophe Chesneau\(^{1,*}\)
\(^{1}\) Department of Mathematics, LMNO, University of Caen-Normandie, 14032 Caen, France.

Copyright © 2024 Christophe Chesneau. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: May 7, 2024 – Accepted: June 28, 2024 – Published: June 30, 2024

Abstract

The study of innovative sequences and series is important in several fields. In this article, we examine the convergence properties of a particular product series that offers adaptability through two parameters and two functions. Based on this analysis, we extend our investigation to a related series. Our main theorems are proved in detail and include several new intermediate results that can be used for other convergence analysis purposes. This is particularly the case for a generalized version of the Riemann sum formula. Several precise examples are presented and discussed, including one related to the gamma function.

Keywords:

mathematical analysis; product sequences; Riemann sum formula; series; Cauchy root convergence rule
]]> Coincidence point results for relational-theoretic contraction mappings in metric spaces with applications https://old.pisrt.org/psr-press/journals/oma-vol-8-issue-1-2024/coincidence-point-results-for-relational-theoretic-contraction-mappings-in-metric-spaces-with-applications/ Sat, 06 Jul 2024 12:22:45 +0000 https://old.pisrt.org/?p=8357
OMA-Vol. 8 (2024), Issue 1, pp. 1 – 17 Open Access Full-Text PDF
Muhammed Raji, Arvind Kumar Rajpoot, Laxmi Rathour, Lakshmi Narayan Mishra and Vishnu Narayan Mishra
Abstract: In this article, we extend the classic Banach contraction principle to a complete metric space equipped with a binary relation. We accomplish this by generalizing several key notions from metric fixed point theory, such as completeness, closedness, continuity, g-continuity, and compatibility, to the relation-theoretic setting. We then use these generalized concepts to prove results on the existence and uniqueness of coincidence points, defined by two mappings acting on a metric space with a binary relation. As a consequence of our main results, we obtain several established metrical coincidence point theorems. We further provide illustrative examples that~demonstrate~the main results. ]]>
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Open Journal of Mathematical Analysis
Vol. 8 (2024), Issue 1, pp. 1 – 17
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2024.0131

Coincidence point results for relational-theoretic contraction mappings in metric spaces with applications

Muhammed Raji\(^{1}\) Arvind Kumar Rajpoot\(^{2}\), Laxmi Rathour\(^{3,*}\), Lakshmi Narayan Mishra\(^{4}\) and Vishnu Narayan Mishra\(^{5}\)
\(^{1}\) Department of Mathematics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria
\(^{2}\) Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
\(^{3}\) Department of Mathematics, National Institute of Technology, Chaltlang, Aizawl 796 012, Mizoram, India
\(^{4}\) Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, Tamil Nadu, India
\(^{5}\) Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484 887, India

Copyright © 2024 Muhammed Raji, Arvind Kumar Rajpoot, Laxmi Rathour, Lakshmi Narayan Mishra and Vishnu Narayan Mishra. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: May 14, 2024 – Accepted: June 6, 2024 – Published: June 30, 2024

Abstract

In this article, we extend the classic Banach contraction principle to a complete metric space equipped with a binary relation. We accomplish this by generalizing several key notions from metric fixed point theory, such as completeness, closedness, continuity, g-continuity, and compatibility, to the relation-theoretic setting. We then use these generalized concepts to prove results on the existence and uniqueness of coincidence points, defined by two mappings acting on a metric space with a binary relation. As a consequence of our main results, we obtain several established metrical coincidence point theorems. We further provide illustrative examples that~demonstrate~the main results.

Keywords:

Coincidence point; binary relations; \(R\)-completeness; \(R\)-continuity; \(R\)-connected sets; \(d\)-self-closedness.
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