Pub Date : 2021-09-30DOI: 10.11568/KJM.2021.29.3.593
S. Kemali, Sevda Sezer, G. Tinaztepe, G. Adi̇lov
In this paper, the concept of $s$-convex function in the third sense is given. Then fundamental characterizations and some basic algebraic properties of $s$-convex function in the third sense are presented. Also, the relations between the third sense $s$-convex functions according to the different values of $s$ are examined.
{"title":"$s$-Convex functions in the third sense","authors":"S. Kemali, Sevda Sezer, G. Tinaztepe, G. Adi̇lov","doi":"10.11568/KJM.2021.29.3.593","DOIUrl":"https://doi.org/10.11568/KJM.2021.29.3.593","url":null,"abstract":"In this paper, the concept of $s$-convex function in the third sense is given. Then fundamental characterizations and some basic algebraic properties of $s$-convex function in the third sense are presented. Also, the relations between the third sense $s$-convex functions according to the different values of $s$ are examined.","PeriodicalId":128912,"journal":{"name":"The Korean Journal of Mathematics","volume":"325 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115343944","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 : 2021-09-30DOI: 10.11568/KJM.2021.29.3.555
Vijayashanthi Palanichamy, J. Kannan
In this paper, we investigate some properties of countably $g$-compact and sequentially GO-compact spaces. Also, we discuss the relation between countably $g$-compact and sequentially GO-compact. Next, we introduce the definition of $g$-subspace and study the characterization of $g$-subspace.
{"title":"On countably $g$-compactness and sequentially GO-compactness","authors":"Vijayashanthi Palanichamy, J. Kannan","doi":"10.11568/KJM.2021.29.3.555","DOIUrl":"https://doi.org/10.11568/KJM.2021.29.3.555","url":null,"abstract":"In this paper, we investigate some properties of countably $g$-compact and sequentially GO-compact spaces. Also, we discuss the relation between countably $g$-compact and sequentially GO-compact. Next, we introduce the definition of $g$-subspace and study the characterization of $g$-subspace.","PeriodicalId":128912,"journal":{"name":"The Korean Journal of Mathematics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134164545","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 : 2021-09-30DOI: 10.11568/KJM.2021.29.3.473
Nityagopal Biswas
In this paper, we investigate the relations between the growth of meromorphic coefficients and that of meromorphic solutions of complex linear differential-difference equations with meromorphic coefficients of finite logarithmic order. Our results can be viewed as the generalization for both the cases of complex linear differential equations and complex linear difference equations.
{"title":"Growth of solutions of linear differential-difference equations with coefficients having the same logarithmic order","authors":"Nityagopal Biswas","doi":"10.11568/KJM.2021.29.3.473","DOIUrl":"https://doi.org/10.11568/KJM.2021.29.3.473","url":null,"abstract":"In this paper, we investigate the relations between the growth of meromorphic coefficients and that of meromorphic solutions of complex linear differential-difference equations with meromorphic coefficients of finite logarithmic order. Our results can be viewed as the generalization for both the cases of complex linear differential equations and complex linear difference equations.","PeriodicalId":128912,"journal":{"name":"The Korean Journal of Mathematics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122371962","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 : 2021-09-30DOI: 10.11568/KJM.2021.29.3.455
K. Das, Krishnadhan Sarkar
Coupled fixed point results have attracted much attention among the researchers in recent times specially in the field of fuzzy metric spaces. In this paper we established a coupled fixed point result for weakly compatible mappings in $G$-fuzzy metric spaces. We have deduced a corollary to our main theorem. Our result also supported by examples.
{"title":"Coupled fixed point results in $G$-fuzzy metric spaces for weakly compatible mappings","authors":"K. Das, Krishnadhan Sarkar","doi":"10.11568/KJM.2021.29.3.455","DOIUrl":"https://doi.org/10.11568/KJM.2021.29.3.455","url":null,"abstract":"Coupled fixed point results have attracted much attention among the researchers in recent times specially in the field of fuzzy metric spaces. In this paper we established a coupled fixed point result for weakly compatible mappings in $G$-fuzzy metric spaces. We have deduced a corollary to our main theorem. Our result also supported by examples.","PeriodicalId":128912,"journal":{"name":"The Korean Journal of Mathematics","volume":"11 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128838125","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 : 2021-09-30DOI: 10.11568/KJM.2021.29.3.467
B. Benaissa
{"title":"On some Copson-type integral inequality","authors":"B. Benaissa","doi":"10.11568/KJM.2021.29.3.467","DOIUrl":"https://doi.org/10.11568/KJM.2021.29.3.467","url":null,"abstract":"","PeriodicalId":128912,"journal":{"name":"The Korean Journal of Mathematics","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128089763","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 : 2021-09-30DOI: 10.11568/KJM.2021.29.3.603
Raeyong Kim
We generalize $3$-manifolds supporting non-positively curved metric to construct manifolds which have the following properties : (1) They are not locally $mathrm{CAT}(0)$. (2) Their fundamental groups are residually finite. (3) They have subgroup separability for some abelian subgroups.
{"title":"Residual finiteness and Abelian subgroup separability of some high dimensional graph manifolds","authors":"Raeyong Kim","doi":"10.11568/KJM.2021.29.3.603","DOIUrl":"https://doi.org/10.11568/KJM.2021.29.3.603","url":null,"abstract":"We generalize $3$-manifolds supporting non-positively curved metric to construct manifolds which have the following properties : (1) They are not locally $mathrm{CAT}(0)$. (2) Their fundamental groups are residually finite. (3) They have subgroup separability for some abelian subgroups.","PeriodicalId":128912,"journal":{"name":"The Korean Journal of Mathematics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126447909","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 : 2021-09-30DOI: 10.11568/KJM.2021.29.3.519
S. Bulut
In a very recent paper, Yousef et al. [Anal. Math. Phys. 11: 58 (2021)] introduced two new subclasses of analytic and bi-univalent functions and obtained the estimates on the first two Taylor-Maclaurin coefficients $leftvert a_{2}rightvert $ and $leftvert a_{3}rightvert $ for functions belonging to these classes. In this study, we introduce a general subclass $mathcal{B}_{Sigma }^{h,p}left( lambda ,mu ,delta right) $ of analytic and bi-univalent functions in the unit disk $mathbb{U}$, and investigate the coefficient bounds for functions belonging to this general function class. Our results improve the results of the above mentioned paper of Yousef et al.
{"title":"Coefficient estimates for a new general subclass of analytic bi-univalent functions","authors":"S. Bulut","doi":"10.11568/KJM.2021.29.3.519","DOIUrl":"https://doi.org/10.11568/KJM.2021.29.3.519","url":null,"abstract":"In a very recent paper, Yousef et al. [Anal. Math. Phys. 11: 58 (2021)] introduced two new subclasses of analytic and bi-univalent functions and obtained the estimates on the first two Taylor-Maclaurin coefficients $leftvert a_{2}rightvert $ and $leftvert a_{3}rightvert $ for functions belonging to these classes. In this study, we introduce a general subclass $mathcal{B}_{Sigma }^{h,p}left( lambda ,mu ,delta right) $ of analytic and bi-univalent functions in the unit disk $mathbb{U}$, and investigate the coefficient bounds for functions belonging to this general function class. Our results improve the results of the above mentioned paper of Yousef et al.","PeriodicalId":128912,"journal":{"name":"The Korean Journal of Mathematics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126437782","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 : 2021-09-30DOI: 10.11568/KJM.2021.29.3.527
Himanshu Kumar
The aim of this article is to give a numerical method for solving Abel's general fuzzy linear integral equations with arbitrary kernel. The method is based on approximations of fractional integrals and Caputo derivatives. The convergence analysis for the proposed method is also given and the applicability of the proposed method is illustrated by solving some numerical examples. The results show the utility and the greater potential of the fractional calculus method to solve fuzzy integral equations.
{"title":"Numerical solution of Abel's general fuzzy linear integral equations by fractional calculus method","authors":"Himanshu Kumar","doi":"10.11568/KJM.2021.29.3.527","DOIUrl":"https://doi.org/10.11568/KJM.2021.29.3.527","url":null,"abstract":"The aim of this article is to give a numerical method for solving Abel's general fuzzy linear integral equations with arbitrary kernel. The method is based on approximations of fractional integrals and Caputo derivatives. The convergence analysis for the proposed method is also given and the applicability of the proposed method is illustrated by solving some numerical examples. The results show the utility and the greater potential of the fractional calculus method to solve fuzzy integral equations.","PeriodicalId":128912,"journal":{"name":"The Korean Journal of Mathematics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126412387","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 : 2021-09-30DOI: 10.11568/KJM.2021.29.3.547
D. Dey
The object of the present paper is to characterize Sasakian 3-manifolds admitting a gradient Ricci-Yamabe soliton. It is shown that a Sasakian 3-manifold $M$ with constant scalar curvature admitting a proper gradient Ricci-Yamabe soliton is Einstein and locally isometric to a unit sphere. Also, the potential vector field is an infinitesimal automorphism of the contact metric structure. In addition, if $M$ is complete, then it is compact.
{"title":"Sasakian 3-manifolds admitting a gradient Ricci-Yamabe soliton","authors":"D. Dey","doi":"10.11568/KJM.2021.29.3.547","DOIUrl":"https://doi.org/10.11568/KJM.2021.29.3.547","url":null,"abstract":"The object of the present paper is to characterize Sasakian 3-manifolds admitting a gradient Ricci-Yamabe soliton. It is shown that a Sasakian 3-manifold $M$ with constant scalar curvature admitting a proper gradient Ricci-Yamabe soliton is Einstein and locally isometric to a unit sphere. Also, the potential vector field is an infinitesimal automorphism of the contact metric structure. In addition, if $M$ is complete, then it is compact.","PeriodicalId":128912,"journal":{"name":"The Korean Journal of Mathematics","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126812183","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 : 2021-09-30DOI: 10.11568/KJM.2021.29.3.501
Ankit Gupta, R. D. Sarma
A uniform study towards normality is provided for topological spaces. Following Cs'{a}sz'{a}r, $gamma$-normality and $gamma$($theta$)-normality are introduced and investigated. For $gamma in Gamma_{13}$, $gamma$-normality is found to satisfy Urysohn's lemma and provide partition of unity. Several existing variants of normality such as $theta$-normality, $Delta$-normality etc. are shown to be particular cases of $gamma$($theta$)-normality. In this process, $gamma$-regularity and $gamma$($theta$)-regularity are introduced and studied. Several important characterizations of all these notions are provided.
{"title":"A generalized approach towards normality for topological spaces","authors":"Ankit Gupta, R. D. Sarma","doi":"10.11568/KJM.2021.29.3.501","DOIUrl":"https://doi.org/10.11568/KJM.2021.29.3.501","url":null,"abstract":"A uniform study towards normality is provided for topological spaces. Following Cs'{a}sz'{a}r, $gamma$-normality and $gamma$($theta$)-normality are introduced and investigated. For $gamma in Gamma_{13}$, $gamma$-normality is found to satisfy Urysohn's lemma and provide partition of unity. Several existing variants of normality such as $theta$-normality, $Delta$-normality etc. are shown to be particular cases of $gamma$($theta$)-normality. In this process, $gamma$-regularity and $gamma$($theta$)-regularity are introduced and studied. Several important characterizations of all these notions are provided.","PeriodicalId":128912,"journal":{"name":"The Korean Journal of Mathematics","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126233372","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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