Pub Date : 2021-11-25DOI: 10.24193/mathcluj.2021.2.12
A. Kashuri, T. Rassias
The authors discover an identity for a generalized integral operator via differentiable function. By using this integral equation, we derive some new bounds on Hermite–Hadamard type integral inequality for differentiable mappings that are in absolute value at certain powers convex. Our results include several new and known results as particular cases. At the end, some applications of presented results for special means and error estimates for the mixed trapezium and midpoint formula have been analyzed. The ideas and techniques of this paper may stimulate further research in the field of integral inequalities.
{"title":"Some new inequalities for convex functions via generalized integral operators and their applications","authors":"A. Kashuri, T. Rassias","doi":"10.24193/mathcluj.2021.2.12","DOIUrl":"https://doi.org/10.24193/mathcluj.2021.2.12","url":null,"abstract":"The authors discover an identity for a generalized integral operator via differentiable function. By using this integral equation, we derive some new bounds on Hermite–Hadamard type integral inequality for differentiable mappings that are in absolute value at certain powers convex. Our results include several new and known results as particular cases. At the end, some applications of presented results for special means and error estimates for the mixed trapezium and midpoint formula have been analyzed. The ideas and techniques of this paper may stimulate further research in the field of integral inequalities.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41995606","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 : 2021-11-25DOI: 10.24193/mathcluj.2021.2.11
M. Houas, Z. Dahmani, E. Set
We study the existence and uniqueness of solutions for integro-differential equations involving two fractional orders. By using the Banach’s fixed point theorem, Leray-Schauder’s nonlinear alternative and Leray-Schauder’s degree theory, the existence and uniqueness of solutions are obtained. Some illustrative examples are also presented.
{"title":"Uniqueness and existence of solutions for nonlinear fractional differential equations with two fractional orders","authors":"M. Houas, Z. Dahmani, E. Set","doi":"10.24193/mathcluj.2021.2.11","DOIUrl":"https://doi.org/10.24193/mathcluj.2021.2.11","url":null,"abstract":"We study the existence and uniqueness of solutions for integro-differential equations involving two fractional orders. By using the Banach’s fixed point theorem, Leray-Schauder’s nonlinear alternative and Leray-Schauder’s degree theory, the existence and uniqueness of solutions are obtained. Some illustrative examples are also presented.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43251011","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 : 2021-11-25DOI: 10.24193/mathcluj.2021.2.02
Z. Bahramian, A. Jabbari
The aim of the present paper is to characterize the strong normal system of the Ellis groups of a well-known family of dynamical systems on the finite and infinite dimensional tori.
本文的目的是在有限维和无限维环面上刻画一类著名动力系统的Ellis群的强正规系统。
{"title":"The strong normal system of some compact right topological groups","authors":"Z. Bahramian, A. Jabbari","doi":"10.24193/mathcluj.2021.2.02","DOIUrl":"https://doi.org/10.24193/mathcluj.2021.2.02","url":null,"abstract":"The aim of the present paper is to characterize the strong normal system of the Ellis groups of a well-known family of dynamical systems on the finite and infinite dimensional tori.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69192279","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 : 2021-11-25DOI: 10.24193/mathcluj.2021.2.05
C. Boonpok
The main goal of this article is to introduce the concepts of *(alpha)-continuous multifunctions and almost *(alpha)-continuous multifunctions. Some characterizations of *(alpha)-continuous multifunctions and almost *(alpha)-continuous multifunctions are established. Furthermore, the relationships between *(alpha)-continuity and almost *(alpha)-continuity are discussed.
{"title":"A study of some forms of continuity for multifunctions in ideal topological spaces","authors":"C. Boonpok","doi":"10.24193/mathcluj.2021.2.05","DOIUrl":"https://doi.org/10.24193/mathcluj.2021.2.05","url":null,"abstract":"The main goal of this article is to introduce the concepts of *(alpha)-continuous multifunctions and almost *(alpha)-continuous multifunctions. Some characterizations of *(alpha)-continuous multifunctions and almost *(alpha)-continuous multifunctions are established. Furthermore, the relationships between *(alpha)-continuity and almost *(alpha)-continuity are discussed.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69192327","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 : 2021-11-25DOI: 10.24193/mathcluj.2021.2.06
A. Boua, A. Abdelwanis
Let R be a prime ring with center Z(R) and alpha,beta be automorphisms of R. This paper is divided into two parts. The first tackles the notions of (generalized) skew derivations on R, as the subject of the present study, several characterization theorems concerning commutativity of prime rings are obtained and an example proving the necessity of the primeness hypothesis of R is given. The second part of the paper tackles the notions of symmetric Jordan bi (alpha,beta)-derivations. In addition, the researchers illustrated that for a prime ring with char(R) different from 2, every symmetric Jordan bi (alpha,alpha)-derivation D of R is a symmetric bi (alpha,alpha)-derivation.
{"title":"Differential identities in prime rings","authors":"A. Boua, A. Abdelwanis","doi":"10.24193/mathcluj.2021.2.06","DOIUrl":"https://doi.org/10.24193/mathcluj.2021.2.06","url":null,"abstract":"Let R be a prime ring with center Z(R) and alpha,beta be automorphisms of R. This paper is divided into two parts. The first tackles the notions of (generalized) skew derivations on R, as the subject of the present study, several characterization theorems concerning commutativity of prime rings are obtained and an example proving the necessity of the primeness hypothesis of R is given. The second part of the paper tackles the notions of symmetric Jordan bi (alpha,beta)-derivations. In addition, the researchers illustrated that for a prime ring with char(R) different from 2, every symmetric Jordan bi (alpha,alpha)-derivation D of R is a symmetric bi (alpha,alpha)-derivation.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46670664","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 : 2021-11-25DOI: 10.24193/mathcluj.2021.2.09
S. Erden, H. Budak, M. Sarıkaya
We establish new perturbed Ostrowski type inequalities for functions whose second derivatives are of bounded variation. In addition, we obtain some integral inequalities for absolutely continuous mappings. Finally, some inequalities related to Lipschitzian derivatives are given.
{"title":"Some perturbed inequalities of Ostrowski type for twice differentiable functions","authors":"S. Erden, H. Budak, M. Sarıkaya","doi":"10.24193/mathcluj.2021.2.09","DOIUrl":"https://doi.org/10.24193/mathcluj.2021.2.09","url":null,"abstract":"We establish new perturbed Ostrowski type inequalities for functions whose second derivatives are of bounded variation. In addition, we obtain some integral inequalities for absolutely continuous mappings. Finally, some inequalities related to Lipschitzian derivatives are given.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49319478","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 : 2021-11-25DOI: 10.24193/mathcluj.2021.2.08
A. Cernea
We study a second-order differential inclusion with integral and multi-strip boundary conditions defined by a set-valued map with nonconvex values. We obtain an existence result and we prove the arcwise connectedness of the solution set of the considered problem.
{"title":"On a second-order differential inclusion with certain integral and multi-strip boundary conditions","authors":"A. Cernea","doi":"10.24193/mathcluj.2021.2.08","DOIUrl":"https://doi.org/10.24193/mathcluj.2021.2.08","url":null,"abstract":"We study a second-order differential inclusion with integral and multi-strip boundary conditions defined by a set-valued map with nonconvex values. We obtain an existence result and we prove the arcwise connectedness of the solution set of the considered problem.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44664547","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 : 2021-11-25DOI: 10.24193/mathcluj.2021.2.04
Hammou Benmehidi, Z. Dahmani
We are concerned with an extension of a coupled sequential differential system of fractional type. Using the Banach contraction principle, we establish new results for the existence and uniqueness of solutions. Then, we prove another existence result via Schaefer’s fixed point theorem. At the end, we illustrate one main result by an example.
{"title":"An extension system of sequential differential equations of arbitrary order","authors":"Hammou Benmehidi, Z. Dahmani","doi":"10.24193/mathcluj.2021.2.04","DOIUrl":"https://doi.org/10.24193/mathcluj.2021.2.04","url":null,"abstract":"We are concerned with an extension of a coupled sequential differential system of fractional type. Using the Banach contraction principle, we establish new results for the existence and uniqueness of solutions. Then, we prove another existence result via Schaefer’s fixed point theorem. At the end, we illustrate one main result by an example.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41847348","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 : 2021-06-30DOI: 10.24193/MATHCLUJ.2021.1.06
Douib Madani, S. Zitouni, Djebabla Abdelhak
We study the well-posedness and asymptotic behaviour of solutions to a laminated beam in thermoelasticity of type III with delay term in the first equation. We show that the system is well-posed by using Lumer-Philips theorem and prove that the system is exponentially stable if and only if the wave speeds are equal.
{"title":"Well-posedness and exponential decay for a laminated beam in thermoelasticity of type III with delay term","authors":"Douib Madani, S. Zitouni, Djebabla Abdelhak","doi":"10.24193/MATHCLUJ.2021.1.06","DOIUrl":"https://doi.org/10.24193/MATHCLUJ.2021.1.06","url":null,"abstract":"We study the well-posedness and asymptotic behaviour of solutions to a laminated beam in thermoelasticity of type III with delay term in the first equation. We show that the system is well-posed by using Lumer-Philips theorem and prove that the system is exponentially stable if and only if the wave speeds are equal.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45029463","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 : 2021-05-20DOI: 10.24193/MATHCLUJ.2021.1.11
S. Șahinkaya, T. C. Quynh
A module theoretic notion of annihilator-stable rings is defined and some characterizations of it are studied.
定义了零化子稳定环的模论概念，并研究了它的一些性质。
{"title":"Kernel stable and uniquely generated modules","authors":"S. Șahinkaya, T. C. Quynh","doi":"10.24193/MATHCLUJ.2021.1.11","DOIUrl":"https://doi.org/10.24193/MATHCLUJ.2021.1.11","url":null,"abstract":"A module theoretic notion of annihilator-stable rings is defined and some characterizations of it are studied.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":"63 (86) 1","pages":"119-127"},"PeriodicalIF":0.0,"publicationDate":"2021-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44049456","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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