OMA – Vol 7 – Issue 2 (2023) – PISRT https://old.pisrt.org Sun, 31 Dec 2023 18:55:01 +0000 en-US hourly 1 https://wordpress.org/?v=6.7 Multiplicity results for a class of nonlinear singular differential equation with a parameter https://old.pisrt.org/psr-press/journals/oma-vol-7-issue-2-2023/multiplicity-results-for-a-class-of-nonlinear-singular-differential-equation-with-a-parameter/ Fri, 29 Dec 2023 12:38:30 +0000 https://old.pisrt.org/?p=8234
OMA-Vol. 7 (2023), Issue 2, pp. 38 – 44 Open Access Full-Text PDF
Shaowen Li
Abstract: This paper gives sufficient conditions for the existence of positive periodic solutions to general indefinite singular differential equations. Furthermore, under some assumptions we show the existence of two positive periodic solutions. The methods used are Krasnoselski\(\breve{\mbox{i}}\)'s-Guo fixed point theorem and the positivity of the associated Green's function.]]>
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Open Journal of Mathematical Analysis
Vol. 7 (2023), Issue 2, pp. 38 – 44
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2023.0130

Multiplicity results for a class of nonlinear singular differential equation with a parameter

Shaowen Li\(^{1,*}\)
\(^{1}\) School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China.

Copyright © 2023 Shaowen Li. 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: June 27, 2023 – Accepted: July 15, 2023 – Published: December 29, 2023

Abstract

This paper gives sufficient conditions for the existence of positive periodic solutions to general indefinite singular differential equations. Furthermore, under some assumptions we show the existence of two positive periodic solutions. The methods used are Krasnoselski\(\breve{\mbox{i}}\)’s-Guo fixed point theorem and the positivity of the associated Green’s function.

Keywords:

Indefinite singularity; Positive periodic solution; Krasnoselski$\breve{\mbox{i}}$’s-Guo fixed point; Green’s function
]]> An introduction to the construction of subfusion frames https://old.pisrt.org/psr-press/journals/oma-vol-7-issue-2-2023/an-introduction-to-the-construction-of-subfusion-frames/ Fri, 29 Dec 2023 12:34:38 +0000 https://old.pisrt.org/?p=8232
OMA-Vol. 7 (2023), Issue 2, pp. 31 – 37 Open Access Full-Text PDF
E. Rahimi and Z. Amiri
Abstract: Fusion frames and subfusion frames are generalizations of frames in the Hilbert spaces. In this paper, we study subfusion frames and the relations between the fusion frames and subfusion frame operators. Also, we introduce new construction of subfusion frames. In particular, we study atomic resolution of the identity on the Hilbert spaces and derive new results.]]>
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Open Journal of Mathematical Analysis
Vol. 7 (2023), Issue 2, pp. 31 – 37
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2023.0129

An Introduction to the Construction of Subfusion Frames

E. Rahimi\(^{1,*}\) and Z. Amiri\(^1\)
\(^{1}\) Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran.
\(^{2}\) Department of Mathematics, Vali-e-Asr University, Rafsanjan, Iran.

Copyright © 2023 E. Rahimi and Z. Amiri. 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: June 27, 2023 – Accepted: July 15, 2023 – Published: December 29, 2023

Abstract

Fusion frames and subfusion frames are generalizations of frames in the Hilbert spaces. In this paper, we study subfusion frames and the relations between the fusion frames and subfusion frame operators. Also, we introduce new construction of subfusion frames. In particular, we study atomic resolution of the identity on the Hilbert spaces and derive new results.

Keywords:

Fusion frames, Subfusion frames, Resolution of the identity.
]]> Upper Estimates For Initial Coefficients and Fekete-Szegö Functional of A Class of Bi-univalent Functions Defined by Means of Subordination and Associated with Horadam Polynomials https://old.pisrt.org/psr-press/journals/oma-vol-7-issue-2-2023/upper-estimates-for-initial-coefficients-and-fekete-szego-functional-of-a-class-of-bi-univalent-functions-defined-by-means-of-subordination-and-associated-with-horadam-polynomials/ Fri, 29 Dec 2023 12:30:01 +0000 https://old.pisrt.org/?p=8230
OMA-Vol. 7 (2023), Issue 2, pp. 21 – 30 Open Access Full-Text PDF
Atinuke Ayanfe Amao and Timothy Oloyede Opoola
Abstract: In this work, a new class of bi-univalent functions \(I^{n+1}_{\Gamma_m,\lambda}(x,z)\) is defined by means of subordination. Upper bounds for some initial coefficients and the Fekete-Szegö functional of functions in the new class were obtained.]]>
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Open Journal of Mathematical Analysis
Vol. 7 (2023), Issue 2, pp. 21- 30
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2023.0128

Upper Estimates For Initial Coefficients and Fekete-Szegö Functional of A Class of Bi-univalent Functions Defined by Means of Subordination and Associated with Horadam Polynomials

Atinuke Ayanfe Amao\(^{1,*}\) and Timothy Oloyede Opoola\(^{1}\)
\(^{1}\) Department of Mathematics, Faculty of Physical Sciences, University of Ilorin. PMB 1515, Ilorin, Nigeria.

Copyright © 2023 Atinuke Ayanfe Amao and Timothy Oloyede Opoola. 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: October 7, 2023 – Accepted: December 2, 2023 – Published: December 29, 2023

Abstract

In this work, a new class of bi-univalent functions \(I^{n+1}_{\Gamma_m,\lambda}(x,z)\) is defined by means of subordination. Upper bounds for some initial coefficients and the Fekete-Szegö functional of functions in the new class were obtained.

Keywords:

Analytic functions,subordination, bi-univalent functions,Höradam polynomial,Opoola differential operator
]]> Some new results of Ostrowski type inequalities using 4-step quadratic kernel and their applications https://old.pisrt.org/psr-press/journals/oma-vol-7-issue-2-2023/some-new-results-of-ostrowski-type-inequalities-using-4-step-quadratic-kernel-and-their-applications/ Fri, 29 Dec 2023 12:26:11 +0000 https://old.pisrt.org/?p=8228
OMA-Vol. 7 (2023), Issue 2, pp. 8 – 20 Open Access Full-Text PDF
Rana Muhammad Kashif Iqbal,Ather Qayyum, ayyaba Nashaiman Atta,Muhammad Moiz Basheer and Ghulam Shabbir
Abstract: This work is a generalization of Ostrowski type integral inequalities using a special 4-step quadratic kernel. Some new and useful results are obtained. Applications to Quadrature Rules and special Probability distribution are also evaluated.]]>
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Open Journal of Mathematical Analysis
Vol. 7 (2023), Issue 2, pp. 8 – 20
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2023.0127

Some new results of ostrowski type inequalities using 4-step quadratic kernel and their applications

Rana Muhammad Kashif Iqbal\(^{1,2,*}\), Ather Qayyum\(^{2}\), Tayyaba Nashaiman Atta\(^{2}\), Muhammad Moiz Basheer\(^{2}\), Ghulam Shabbir\(^{3}\)
\(^{1}\)Department of Mathematics, Institute of Southern Punjab, Multan Pakistan.
\(^{2}\)Department of Mathematics, Institute of Southern Punjab, Multan Pakistan.
\(^{3}\)Department of Mathematics, University of Agriculture Faisalabad, Pakistan.

Copyright © 2023 Rana Muhammad Kashif Iqbal,Ather Qayyum, ayyaba Nashaiman Atta,Muhammad Moiz Basheer and Ghulam Shabbir. 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: August 10, 2023 – Accepted: December 2, 2023 – Published: December 29, 2023

Abstract

This work is a generalization of Ostrowski type integral inequalities using
a special 4-step quadratic kernel. Some new and useful results are obtained.
Applications to Quadrature Rules and special Probability distribution are
also evaluated.

Keywords:

Coefficient bounds; Fekete-Szego inequalities; \(p\)-valent functions
]]> Floquet exponent of solution to homogeneous growth-fragmentation equation https://old.pisrt.org/psr-press/journals/oma-vol-7-issue-2-2023/floquet-exponent-of-solution-to-homogeneous-growth-fragmentation-equation/ Fri, 29 Dec 2023 12:22:46 +0000 https://old.pisrt.org/?p=8226
OMA-Vol. 7 (2023), Issue 2, pp. 1 – 7 Open Access Full-Text PDF
MEAS Len
Abstract: In this work, we establish the existence and uniqueness of solution of Floquet eigenvalue and its adjoint to homogeneous growth-fragmentation equation with positive and periodic coefficients. We study the Floquet exponent, which measures the growth rate of a population. Finally, we establish the long term behavior of solution to the homogeneous growth-fragmentation equation by entropy method [1,2,3].]]>
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Open Journal of Mathematical Analysis
Vol. 7 (2023), Issue 2, pp. 1 – 7
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2023.0126

Floquet Exponent of Solution to Homogeneous Growth-Fragmentation Equation

MEAS Len\(^{1,*}\)
\(^{1}\) Department of Mathematics, Royal University of Phnom Penh, Phnom Penh, Cambodia.

Copyright © 2023 MEAS Len. 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: September 22, 2023 – Accepted: December 2, 2023 – Published: December 29, 2023

Abstract

In this work, we establish the existence and uniqueness of solution of Floquet eigenvalue and its adjoint to homogeneous growth-fragmentation equation with positive and periodic coefficients. We study the Floquet exponent, which measures the growth rate of a population. Finally, we establish the long term behavior of solution to the homogeneous growth-fragmentation equation by entropy method [1,2,3].

Keywords:

Homogeneous Growth-Fragmentation Equation; Floquet theory; Entropy method
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