Pub Date : 2023-06-30DOI: 10.30538/psrp-oma2023.0122
Obogi Robert Karieko
In this paper, we concentrate on norms of derivations implemented by self-adjoint operators. We determine the upper and lower norm estimates of derivations implemented by self-adjoint operators.The results show that the knowledge of self-adjoint governs the quantum chemical system in which the eigenvalue and eigenvector of a self-adjoint operator represents the ground state energy and the ground state wave function of the system respectively.
{"title":"On norms of derivations implemented by self-adjoint operators","authors":"Obogi Robert Karieko","doi":"10.30538/psrp-oma2023.0122","DOIUrl":"https://doi.org/10.30538/psrp-oma2023.0122","url":null,"abstract":"In this paper, we concentrate on norms of derivations implemented by self-adjoint operators. We determine the upper and lower norm estimates of derivations implemented by self-adjoint operators.The results show that the knowledge of self-adjoint governs the quantum chemical system in which the eigenvalue and eigenvector of a self-adjoint operator represents the ground state energy and the ground state wave function of the system respectively.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139366263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-30DOI: 10.30538/psrp-oma2023.0125
Olusegun Awoyale, T. Opoola
This present paper introduces two new subclasses of p-valent functions. The coefficient bounds and Fekete-Szego inequalities for the functions in these classes are also obtained.
本文介绍了 p 值函数的两个新子类。同时还得到了这两类函数的系数边界和 Fekete-Szego 不等式。
{"title":"Coefficient bounds for (p)-valent functions","authors":"Olusegun Awoyale, T. Opoola","doi":"10.30538/psrp-oma2023.0125","DOIUrl":"https://doi.org/10.30538/psrp-oma2023.0125","url":null,"abstract":"This present paper introduces two new subclasses of p-valent functions. The coefficient bounds and Fekete-Szego inequalities for the functions in these classes are also obtained.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139366768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-30DOI: 10.30538/psrp-oma2022.0108
Hongwei Zhang, Huiru Ji
This work is devoted to study the global solutions of a class of nonlinear Moore-Gibson-Thompson equation. By applying the Galerkin and compact methods, we derive some sufficient conditions on the nonlinear terms, which lead to the existence and uniqueness of the global solution.
{"title":"On global solutions of the nonlinear Moore-Gibson-Thompson equation","authors":"Hongwei Zhang, Huiru Ji","doi":"10.30538/psrp-oma2022.0108","DOIUrl":"https://doi.org/10.30538/psrp-oma2022.0108","url":null,"abstract":"This work is devoted to study the global solutions of a class of nonlinear Moore-Gibson-Thompson equation. By applying the Galerkin and compact methods, we derive some sufficient conditions on the nonlinear terms, which lead to the existence and uniqueness of the global solution.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45153070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-22DOI: 10.30538/psrp-oma2022.0107
Benard Okelo, Jeffar Oburu
This work is an in-depth study of the class of norm-attainable operators in a general Banach space setting. We give characterizations of norm-attainable operators on involutive stereotype tubes with algebraically connected component of the identity. In particular, we prove reflexivity, boundedness and compactness properties when the set of these operators contains unit balls with involution for the tubes when they are of stereotype category
{"title":"Norm-attainable operators on involutive stereotype tubes with algebraically connected component of the identity","authors":"Benard Okelo, Jeffar Oburu","doi":"10.30538/psrp-oma2022.0107","DOIUrl":"https://doi.org/10.30538/psrp-oma2022.0107","url":null,"abstract":"This work is an in-depth study of the class of norm-attainable operators in a general Banach space setting. We give characterizations of norm-attainable operators on involutive stereotype tubes with algebraically connected component of the identity. In particular, we prove reflexivity, boundedness and compactness properties when the set of these operators contains unit balls with involution for the tubes when they are of stereotype category","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44862623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-21DOI: 10.30538/psrp-oma2022.0103
Kwancheol Shin, Ju Han Changwon Yoon
In this paper, we investigate some properties of the (AP)-Henstock integral on a compact set and prove that the product of an (AP)-Henstock integrable function and a function of bounded variation is (AP)-Henstock integrable. Furthermore, we prove that the product of an (AP)-Henstock integrable function and a regulated function is also (AP)-Henstock integrable. We also define the (AP)-Henstock integral on an unbounded interval, investigate some properties, and show similar multiplier properties.
{"title":"Multiplier properties for the (AP)-Henstock integral","authors":"Kwancheol Shin, Ju Han Changwon Yoon","doi":"10.30538/psrp-oma2022.0103","DOIUrl":"https://doi.org/10.30538/psrp-oma2022.0103","url":null,"abstract":"In this paper, we investigate some properties of the (AP)-Henstock integral on a compact set and prove that the product of an (AP)-Henstock integrable function and a function of bounded variation is (AP)-Henstock integrable. Furthermore, we prove that the product of an (AP)-Henstock integrable function and a regulated function is also (AP)-Henstock integrable. We also define the (AP)-Henstock integral on an unbounded interval, investigate some properties, and show similar multiplier properties.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47760136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-21DOI: 10.30538/psrp-oma2022.0102
A. Y. Akinyele, Omotoni Ezekiel Jimoh, J. Omosowon, Liman Kinbokun Alhassan, K. A. Bello
This paper consists of the results about (omega)-order preserving partial contraction mapping using perturbation theory to generate a one-parameter semigroup. We show that adding a bounded linear operator (B) to an infinitesimal generator (A) of a semigroup of the linear operator does not destroy A's property. Furthermore, (A) is the generator of a one-parameter semigroup, and (B) is a small perturbation so that (A+B) is also the generator of a one-parameter semigroup.
{"title":"Results of a perturbation theory generating a one-parameter semigroup","authors":"A. Y. Akinyele, Omotoni Ezekiel Jimoh, J. Omosowon, Liman Kinbokun Alhassan, K. A. Bello","doi":"10.30538/psrp-oma2022.0102","DOIUrl":"https://doi.org/10.30538/psrp-oma2022.0102","url":null,"abstract":"This paper consists of the results about (omega)-order preserving partial contraction mapping using perturbation theory to generate a one-parameter semigroup. We show that adding a bounded linear operator (B) to an infinitesimal generator (A) of a semigroup of the linear operator does not destroy A's property. Furthermore, (A) is the generator of a one-parameter semigroup, and (B) is a small perturbation so that (A+B) is also the generator of a one-parameter semigroup.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47872436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-21DOI: 10.30538/psrp-oma2022.0105
A. Al‐Mahdi, M. Al‐Gharabli
In this paper we consider the following abstract class of weakly dissipative second-order systems with infinite memory, (u''(t)+Au(t)-displaystyleint_{0}^{infty} g(s)A^alpha u(t-s)ds=0,~t>0,) and establish a general stability result with a very general assumption on the behavior of (g) at infinity; that is (g'(t) leq - xi(t) G left(g(t)right),~~t geq 0.) where (xi) and (G) are two functions satisfying some specific conditions. Our result generalizes and improves many earlier results in the literature. Moreover, we obtain our result with imposing a weaker restrictive assumption on the boundedness of initial data used in many earlier papers in the literature such as the one in [1,2,3,4,5]. The proof is based on the energy method together with convexity arguments.
在本文中，我们考虑了以下抽象类具有无穷大记忆的弱耗散二阶系统，（u’’（t）+Au（t）-displaystyleint_｛0｝^｛infty｝g（s）A^alphau（t-s）ds=0，~t>0，），并用一个关于（g）在无穷大处行为的一般假设建立了一个一般稳定性结果；即（g'（t）leq-neneneba xi（t）gleft（g（t） right），~~~tgeq0.），其中（nenenebb xi ）和（g）是满足某些特定条件的两个函数。我们的结果推广和改进了文献中许多早期的结果。此外，我们通过对文献中许多早期论文（如[1，2，3，4，5]中的论文）中使用的初始数据的有界性施加较弱的限制性假设来获得我们的结果。该证明基于能量法和凸性论证。
{"title":"Stability result for a class of weakly dissipative second-order systems with infinite memory","authors":"A. Al‐Mahdi, M. Al‐Gharabli","doi":"10.30538/psrp-oma2022.0105","DOIUrl":"https://doi.org/10.30538/psrp-oma2022.0105","url":null,"abstract":"In this paper we consider the following abstract class of weakly dissipative second-order systems with infinite memory, (u''(t)+Au(t)-displaystyleint_{0}^{infty} g(s)A^alpha u(t-s)ds=0,~t>0,) and establish a general stability result with a very general assumption on the behavior of (g) at infinity; that is (g'(t) leq - xi(t) G left(g(t)right),~~t geq 0.) where (xi) and (G) are two functions satisfying some specific conditions. Our result generalizes and improves many earlier results in the literature. Moreover, we obtain our result with imposing a weaker restrictive assumption on the boundedness of initial data used in many earlier papers in the literature such as the one in [1,2,3,4,5]. The proof is based on the energy method together with convexity arguments.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43456272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-21DOI: 10.30538/psrp-oma2022.0104
Tuğrul Cömert, E. Pişkin
In this paper, we study the initial boundary value problem for a p-biharmonic parabolic equation with logarithmic nonlinearity. By using the potential wells method and logarithmic Sobolev inequality, we obtain the existence of the unique global weak solution. In addition, we also obtain decay polynomially of solutions.
{"title":"Global existence and decay of solutions for p-biharmonic parabolic equation with logarithmic nonlinearity","authors":"Tuğrul Cömert, E. Pişkin","doi":"10.30538/psrp-oma2022.0104","DOIUrl":"https://doi.org/10.30538/psrp-oma2022.0104","url":null,"abstract":"In this paper, we study the initial boundary value problem for a p-biharmonic parabolic equation with logarithmic nonlinearity. By using the potential wells method and logarithmic Sobolev inequality, we obtain the existence of the unique global weak solution. In addition, we also obtain decay polynomially of solutions.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46528831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-21DOI: 10.30538/psrp-oma2022.0101
Rajan Puri
We consider 1D and 2D Schrödinger equation with delta potential on the positive half-axis with Dirichlet, Neumann, and Robin type boundary conditions. We presented and estimated the exact values of the beta critical.
{"title":"Beta critical of Schrödinger operator with delta potential in one and two dimension","authors":"Rajan Puri","doi":"10.30538/psrp-oma2022.0101","DOIUrl":"https://doi.org/10.30538/psrp-oma2022.0101","url":null,"abstract":"We consider 1D and 2D Schrödinger equation with delta potential on the positive half-axis with Dirichlet, Neumann, and Robin type boundary conditions. We presented and estimated the exact values of the beta critical.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42495813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-21DOI: 10.30538/psrp-oma2022.0099
Santosh Ghimire
The martingale analogue of Kolmogorov’s law of the iterated logarithm was obtained by W. Stout using probabilistic approach. In this paper, we give a new proof of one side of the same law of the iterated logarithm for dyadic martingale using subgaussian type estimates and Borel-Cantelli Lemma.
{"title":"One-sided law of the iterated logarithm for dyadic martingale using sub-gaussian estimates","authors":"Santosh Ghimire","doi":"10.30538/psrp-oma2022.0099","DOIUrl":"https://doi.org/10.30538/psrp-oma2022.0099","url":null,"abstract":"The martingale analogue of Kolmogorov’s law of the iterated logarithm was obtained by W. Stout using probabilistic approach. In this paper, we give a new proof of one side of the same law of the iterated logarithm for dyadic martingale using subgaussian type estimates and Borel-Cantelli Lemma.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41322665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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