Pub Date : 2021-08-01DOI: 10.32513/tmj/19322008145
Ashok Rathod
In this paper, we investigate the uniqueness of meromorphic functions sharing a set with counting multiplicity and also with weight 1 in an angular domain.
在本文中，我们研究了在角域中共享一个具有计数多重性和权重为1的集合的亚纯函数的唯一性。
{"title":"The shared set and uniqueness of meromorphic functions in an angular domain","authors":"Ashok Rathod","doi":"10.32513/tmj/19322008145","DOIUrl":"https://doi.org/10.32513/tmj/19322008145","url":null,"abstract":"In this paper, we investigate the uniqueness of meromorphic functions sharing a set with counting multiplicity and also with weight 1 in an angular domain.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42806770","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 : 2021-08-01DOI: 10.32513/tmj/19322008150
S. Maghsoodi, A. Neamaty
In this research, we intend to show that the nonlocal fractional Cauchy problem Dαu(t)=A(t)u(t)+f(t,u(t)), t∈J=[0,1] with integral initial condition u(0)=∫01g(s,u(s))ds, in the Banach space X, where A is a generator of α-resolvent operator function {T(t)}t≥0 and f, g are given functions satisfying some assumptions, has an almost periodic solution.
{"title":"Existence of almost periodic solution for nonlocal fractional Cauchy problem with integral initial condition","authors":"S. Maghsoodi, A. Neamaty","doi":"10.32513/tmj/19322008150","DOIUrl":"https://doi.org/10.32513/tmj/19322008150","url":null,"abstract":"In this research, we intend to show that the nonlocal fractional Cauchy problem Dαu(t)=A(t)u(t)+f(t,u(t)), t∈J=[0,1] with integral initial condition u(0)=∫01g(s,u(s))ds, in the Banach space X, where A is a generator of α-resolvent operator function {T(t)}t≥0 and f, g are given functions satisfying some assumptions, has an almost periodic solution.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42917892","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 : 2021-08-01DOI: 10.32513/tmj/19322008156
F. M. A. Mashhad
Let R be an associative ring with identity and M be a left R-module. In this paper, we introduce M-Gorenstein injective modules as a generalization of Gorenstein injective modules. We verify some properties of M-Gorenstein injective modules analogous to those holding for Gorenstein injective modules. There is an interesting theorem in classical homological algebra which asserts that R is a Noetherian ring if and only if the class of injective modules over R is closed under arbitrary direct sum. Our goal in this paper is to investigate the M-Gorenstein injective counterpart of this fact. If the class of M-Gorenstein injective modules over R is closed under arbitrary direct sum, then R will be a Noetherian ring. Also, it has been proved that in the special case M=R, when R is a commutative Noetherian ring with a dualizing complex, then the class of R-Gorenstein injective modules is closed under arbitrary direct sum. In the main theorem of this paper, we prove the general case of this result. More precisely, we show that for any left R-module M over a Noetherian ring R in which every R-module has finite M-Gorenstein injective dimension, the class of M-Gorenstein injective modules is closed under arbitrary direct sum.
{"title":"A generalization of Gorenstein injective modules","authors":"F. M. A. Mashhad","doi":"10.32513/tmj/19322008156","DOIUrl":"https://doi.org/10.32513/tmj/19322008156","url":null,"abstract":"Let R be an associative ring with identity and M be a left R-module. In this paper, we introduce M-Gorenstein injective modules as a generalization of Gorenstein injective modules. We verify some properties of M-Gorenstein injective modules analogous to those holding for Gorenstein injective modules. There is an interesting theorem in classical homological algebra which asserts that R is a Noetherian ring if and only if the class of injective modules over R is closed under arbitrary direct sum. Our goal in this paper is to investigate the M-Gorenstein injective counterpart of this fact. If the class of M-Gorenstein injective modules over R is closed under arbitrary direct sum, then R will be a Noetherian ring. Also, it has been proved that in the special case M=R, when R is a commutative Noetherian ring with a dualizing complex, then the class of R-Gorenstein injective modules is closed under arbitrary direct sum. In the main theorem of this paper, we prove the general case of this result. More precisely, we show that for any left R-module M over a Noetherian ring R in which every R-module has finite M-Gorenstein injective dimension, the class of M-Gorenstein injective modules is closed under arbitrary direct sum.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42180610","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 : 2021-08-01DOI: 10.32513/tmj/19322008148
O. Mukhtarov, S. Çavuşoğlu, P. Pandey
The purpose of this study is to present a new modification of finite difference method (FDM) for approximating the solution of the two-interval boundary value problems for second order differential equations, whose main feature is the nature of the imposed conditions. Namely, the investigated problems contains not only boundary conditions at the points of the considered interval, but also an additional conditions at one interior point of interaction, so-called transmission conditions. Naturally, the analysis of two-interval boundary-value problems is more complicated and it is not clear how to extend the classical FDM to such type problems. The proposed modification of FDM tested on two model problems with known exact solutions. The obtained result are illustrate the applicability and efficiency of our own algoritm, which can be readily extended to all many-interval problems.
{"title":"Development of the Finite Difference Method to solve a new type Sturm-Liouville problems","authors":"O. Mukhtarov, S. Çavuşoğlu, P. Pandey","doi":"10.32513/tmj/19322008148","DOIUrl":"https://doi.org/10.32513/tmj/19322008148","url":null,"abstract":"The purpose of this study is to present a new modification of finite difference method (FDM) for approximating the solution of the two-interval boundary value problems for second order differential equations, whose main feature is the nature of the imposed conditions. Namely, the investigated problems contains not only boundary conditions at the points of the considered interval, but also an additional conditions at one interior point of interaction, so-called transmission conditions. Naturally, the analysis of two-interval boundary-value problems is more complicated and it is not clear how to extend the classical FDM to such type problems. The proposed modification of FDM tested on two model problems with known exact solutions. The obtained result are illustrate the applicability and efficiency of our own algoritm, which can be readily extended to all many-interval problems.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43475190","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 : 2021-08-01DOI: 10.32513/tmj/19322008146
Dipankar Das, V. Mishra, L. Mishra
In this paper, we introduce C*-algebra valued modular S-metric spaces. Some common fixed point results for S-weak operator pair on C*-algebra valued modular S-metric spaces is given with suitable examples. Stability of the fixed point and application for a system of integral equations are also discussed here.
{"title":"C*-algebra valued modular S-metric spaces with applications in fixed point theory","authors":"Dipankar Das, V. Mishra, L. Mishra","doi":"10.32513/tmj/19322008146","DOIUrl":"https://doi.org/10.32513/tmj/19322008146","url":null,"abstract":"In this paper, we introduce C*-algebra valued modular S-metric spaces. Some common fixed point results for S-weak operator pair on C*-algebra valued modular S-metric spaces is given with suitable examples. Stability of the fixed point and application for a system of integral equations are also discussed here.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44035901","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 : 2021-08-01DOI: 10.32513/tmj/19322008149
S. Aslanci, Tarana Sultanova
Using holomorphic extensions of functions, we introduce so-called deformed lifts in the tangent bundle of two order being defined as the set of all higher order 2-jets and investigate some properties of these lifts.
{"title":"Deformed lifts in the bundle of 2-jets","authors":"S. Aslanci, Tarana Sultanova","doi":"10.32513/tmj/19322008149","DOIUrl":"https://doi.org/10.32513/tmj/19322008149","url":null,"abstract":"Using holomorphic extensions of functions, we introduce so-called deformed lifts in the tangent bundle of two order being defined as the set of all higher order 2-jets and investigate some properties of these lifts.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49597971","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 : 2021-08-01DOI: 10.32513/tmj/19322008141
K. R. Laxmi, R. B. Sharma
In this paper we have discussed about second Hankel determinant of Ma-Minda starlike bi-univalent and Ma-Minda convex bi-univalent functions in the open unit disc Δ subordinate to a starlike univalent function whose range is symmetric with respect to the real axis involving the Fekete-Szego parameter λ.
{"title":"Second Hankel determinant with Fekete-Szegö parameter for some subclasses of bi-univalent functions using a symmetric q-derivative operator","authors":"K. R. Laxmi, R. B. Sharma","doi":"10.32513/tmj/19322008141","DOIUrl":"https://doi.org/10.32513/tmj/19322008141","url":null,"abstract":"In this paper we have discussed about second Hankel determinant of Ma-Minda starlike bi-univalent and Ma-Minda convex bi-univalent functions in the open unit disc Δ subordinate to a starlike univalent function whose range is symmetric with respect to the real axis involving the Fekete-Szego parameter λ.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46073671","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 : 2021-08-01DOI: 10.32513/tmj/19322008151
H. Arabyani
Schur proved that if G is a group such that G/Z(G) is finite, then G′ is finite. Several authors studied the converse of Schur’s theorem. In this paper, we extend the converse of Schur’s theorem to a pair of groups. Also, we determine the structure of a pairs of groups under some conditions.
{"title":"The commutator subgroup of a pair of groups","authors":"H. Arabyani","doi":"10.32513/tmj/19322008151","DOIUrl":"https://doi.org/10.32513/tmj/19322008151","url":null,"abstract":"Schur proved that if G is a group such that G/Z(G) is finite, then G′ is finite. Several authors studied the converse of Schur’s theorem. In this paper, we extend the converse of Schur’s theorem to a pair of groups. Also, we determine the structure of a pairs of groups under some conditions.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46109781","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 : 2021-06-01DOI: 10.32513/tmj/19322008127
S. Harikrishnan, K. Kanagarajan, E. Elsayed
In this paper, we investigate the existence of solution for not instantaneous impulsive fractional differential equations with random parameter. By using fixed point theorems, we establish sufficient conditions for the existence and uniqueness of solutions. Finally, generalized Ulam Hyers Rassias stable solution is also obtained.
{"title":"Study on fractional random differential equations with not instantaneous impulses","authors":"S. Harikrishnan, K. Kanagarajan, E. Elsayed","doi":"10.32513/tmj/19322008127","DOIUrl":"https://doi.org/10.32513/tmj/19322008127","url":null,"abstract":"In this paper, we investigate the existence of solution for not instantaneous impulsive fractional differential equations with random parameter. By using fixed point theorems, we establish sufficient conditions for the existence and uniqueness of solutions. Finally, generalized Ulam Hyers Rassias stable solution is also obtained.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49075514","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 : 2021-06-01DOI: 10.32513/tmj/19322008137
S. Mehmood, F. Zafar, M. Latif, N. Yasmin
In this paper, some new estimates of Hermite-Hadamard-Fejer inequality for $n$-times differentiable preinvex functions are established. It is noteworthy that the weighted estimates of the left and right hand side of the Hermite-Hadamard inequalities involving generalized preinvex functions doesn't exist previously.
{"title":"Fejér-Hermite-Hadamard inequalities for $n$-times differentiable preinvex functions","authors":"S. Mehmood, F. Zafar, M. Latif, N. Yasmin","doi":"10.32513/tmj/19322008137","DOIUrl":"https://doi.org/10.32513/tmj/19322008137","url":null,"abstract":"In this paper, some new estimates of Hermite-Hadamard-Fejer inequality for $n$-times differentiable preinvex functions are established. It is noteworthy that the weighted estimates of the left and right hand side of the Hermite-Hadamard inequalities involving generalized preinvex functions doesn't exist previously.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45462198","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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