Pub Date : 2020-12-01DOI: 10.32513/tbilisi/1608606056
Y. Soykan, Nejla Özmen, Melih Göcen
In this paper, we introduce the generalized Pentanacci quaternions and we present Binet's formulas, generating functions and the summation formulas for these quaternions and as special case for Pentanacci and Pentanacci-Lucas quaternions. Furthermore, we present matrices related to generalized Pentanacci quaternions.
{"title":"On generalized Pentanacci quaternions","authors":"Y. Soykan, Nejla Özmen, Melih Göcen","doi":"10.32513/tbilisi/1608606056","DOIUrl":"https://doi.org/10.32513/tbilisi/1608606056","url":null,"abstract":"In this paper, we introduce the generalized Pentanacci quaternions and we present Binet's formulas, generating functions and the summation formulas for these quaternions and as special case for Pentanacci and Pentanacci-Lucas quaternions. Furthermore, we present matrices related to generalized Pentanacci quaternions.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47877795","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 : 2020-12-01DOI: 10.32513/tbilisi/1608606057
Y. Khatib, M. Hassani, M. Amyari
{"title":"An extension of the operator Kantorovich inequality","authors":"Y. Khatib, M. Hassani, M. Amyari","doi":"10.32513/tbilisi/1608606057","DOIUrl":"https://doi.org/10.32513/tbilisi/1608606057","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44266707","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 : 2020-12-01DOI: 10.32513/tbilisi/1608606054
P. Jain, C. Basu, V. Panwar
In this paper a new generalization of $B^*$-continuity has been defined, to be called as $B^*$-clopen continuity and many of its properties have been studied including the convergence behaviour of sequences of such functions. Also a new type of oscillation function, called cl-oscillation has been defined, which characterizes the $B^*$-clopen continuity.
{"title":"On $B^*$-clopen continuity, oscillation and convergence","authors":"P. Jain, C. Basu, V. Panwar","doi":"10.32513/tbilisi/1608606054","DOIUrl":"https://doi.org/10.32513/tbilisi/1608606054","url":null,"abstract":"In this paper a new generalization of $B^*$-continuity has been defined, to be called as $B^*$-clopen continuity and many of its properties have been studied including the convergence behaviour of sequences of such functions. Also a new type of oscillation function, called cl-oscillation has been defined, which characterizes the $B^*$-clopen continuity.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45751510","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 : 2020-12-01DOI: 10.32513/tbilisi/1608606052
D. Caratelli, P. Ricci
{"title":"A note on integer powers of a companion matrix and applications","authors":"D. Caratelli, P. Ricci","doi":"10.32513/tbilisi/1608606052","DOIUrl":"https://doi.org/10.32513/tbilisi/1608606052","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43334040","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 : 2020-12-01DOI: 10.32513/tbilisi/1608606045
B. Venkateswarlu, P. Reddy, N. Rani
In this paper we introduce and study a new subclass of meromorphically uniformly convex functions with positive coefficients defined by a differential operator and obtain coefficient estimates, growth and distortion theorem, radius of convexity,integral transforms, convex linear combinations, convolution properties and $delta$-neighborhoods for the class $Sigma_{p}(alpha , beta )$.
{"title":"Certain subclass of meromorphic functions involving generalized differential operator","authors":"B. Venkateswarlu, P. Reddy, N. Rani","doi":"10.32513/tbilisi/1608606045","DOIUrl":"https://doi.org/10.32513/tbilisi/1608606045","url":null,"abstract":"In this paper we introduce and study a new subclass of meromorphically uniformly convex functions with positive coefficients defined by a differential operator and obtain coefficient estimates, growth and distortion theorem, radius of convexity,integral transforms, convex linear combinations, convolution properties and $delta$-neighborhoods for the class $Sigma_{p}(alpha , beta )$.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43610564","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 : 2020-12-01DOI: 10.32513/tbilisi/1608606058
K. R. Prasad, M. Khuddush, D. Leela
{"title":"Existence of solutions for infinite systems of regular fractional Sturm-Liouville problems in the spaces of tempered sequences","authors":"K. R. Prasad, M. Khuddush, D. Leela","doi":"10.32513/tbilisi/1608606058","DOIUrl":"https://doi.org/10.32513/tbilisi/1608606058","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48317875","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 : 2020-12-01DOI: 10.32513/tbilisi/1608606046
A. Raj, S. Pinelas, P. DivyaKumari
{"title":"Hyers-Ulam stability quintic functional equation in F-spaces: direct method","authors":"A. Raj, S. Pinelas, P. DivyaKumari","doi":"10.32513/tbilisi/1608606046","DOIUrl":"https://doi.org/10.32513/tbilisi/1608606046","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43025101","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 : 2020-12-01DOI: 10.32513/tbilisi/1608606059
Xianwen Xie, Hou-biao Li
In this paper, a lopsided modified Euler-extrapolated Hermitian and skew-Hermitian splitting (LME-HS) iteration method is introduced for solving the complex symmetric linear systems. Under a loose restriction on parameter $theta$, we demonstrate that LME-HS iteration method is convergent. Moreover, we present the optimal parameter ${theta}^{*}$ of the LME-HS method and discuss the spectral properties of corresponding preconditioned matrix. Finally, the numerical experiments are used to verify the effectiveness of the proposed method.
{"title":"Lopsided modified Euler-extrapolated Hermitian and skew-Hermitian splitting method for a class of complex symmetric linear systems","authors":"Xianwen Xie, Hou-biao Li","doi":"10.32513/tbilisi/1608606059","DOIUrl":"https://doi.org/10.32513/tbilisi/1608606059","url":null,"abstract":"In this paper, a lopsided modified Euler-extrapolated Hermitian and skew-Hermitian splitting (LME-HS) iteration method is introduced for solving the complex symmetric linear systems. Under a loose restriction on parameter $theta$, we demonstrate that LME-HS iteration method is convergent. Moreover, we present the optimal parameter ${theta}^{*}$ of the LME-HS method and discuss the spectral properties of corresponding preconditioned matrix. Finally, the numerical experiments are used to verify the effectiveness of the proposed method.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43989060","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 : 2020-09-01DOI: 10.32513/tbilisi/1601344902
S. Şenyurt, Burak Öztürk
{"title":"Smarandache curves according to the Sabban frame belonging to spherical indicatrix curve of the Salkowski curve","authors":"S. Şenyurt, Burak Öztürk","doi":"10.32513/tbilisi/1601344902","DOIUrl":"https://doi.org/10.32513/tbilisi/1601344902","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43453729","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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