{"title":"Weighted Pál type (1;0)-interpolation on the zeros of Laguerre\u0000 abscissas","authors":"Neha Mathur, P. Mathur","doi":"10.32513/TMJ/1932200818","DOIUrl":"https://doi.org/10.32513/TMJ/1932200818","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45817256","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 : 2021-03-01DOI: 10.32513/TMJ/19322008110
Haşim Çayır
{"title":"The transformation of the involute curves using by lifts on\u0000 $R^{3}$ to tangent space $TR^{3}$","authors":"Haşim Çayır","doi":"10.32513/TMJ/19322008110","DOIUrl":"https://doi.org/10.32513/TMJ/19322008110","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43583607","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 : 2021-03-01DOI: 10.32513/TMJ/19322008114
H. Özarslan, A. Karakas
{"title":"A new note on absolute matrix summability of infinite\u0000 series","authors":"H. Özarslan, A. Karakas","doi":"10.32513/TMJ/19322008114","DOIUrl":"https://doi.org/10.32513/TMJ/19322008114","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"14 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41450734","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}
{"title":"Coefficient inequalities of analytic functions equipped with\u0000 conic domains involving $q$-analogue of Noor integral operator","authors":"K. Noor, Ş. Altınkaya, S. Yalçın","doi":"10.32513/TMJ/1932200811","DOIUrl":"https://doi.org/10.32513/TMJ/1932200811","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41586530","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}
{"title":"Existence and uniqueness of solutions to anti-periodic\u0000 Riezs-Caputo impulsive fractional boundary value problems","authors":"Şuayip Toprakseven","doi":"10.32513/TMJ/1932200816","DOIUrl":"https://doi.org/10.32513/TMJ/1932200816","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45716825","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/1608606051
S. Mallick
In this paper, we prove the existence of non-critically injective polynomials whose set of zeros form unique range sets that answers one of the most awaited and fundamental questions of uniqueness theory of entire and meromorphic functions. We also show that there exist some unique range sets and their generating polynomials which can not be characterized by any of the existing generalized results of unique range sets but as an application of our main theorems the same can be characterized. Moreover, as an application of our main results we prove that the cardinality of a unique range set does not always depend upon the number of distinct critical points of its generating polynomial.
{"title":"On the existence of unique range sets generated by non-critically injective polynomials and related issues","authors":"S. Mallick","doi":"10.32513/tbilisi/1608606051","DOIUrl":"https://doi.org/10.32513/tbilisi/1608606051","url":null,"abstract":"In this paper, we prove the existence of non-critically injective polynomials whose set of zeros form unique range sets that answers one of the most awaited and fundamental questions of uniqueness theory of entire and meromorphic functions. We also show that there exist some unique range sets and their generating polynomials which can not be characterized by any of the existing generalized results of unique range sets but as an application of our main theorems the same can be characterized. Moreover, as an application of our main results we prove that the cardinality of a unique range set does not always depend upon the number of distinct critical points of its generating polynomial.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"13 1","pages":"81-101"},"PeriodicalIF":0.5,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43062663","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/1608606055
Tingfu Ma, Y. Ge
In this article, firstly, based on Taylor series expansion and truncation error correction technology, combined with the fourth-order Pade schemes of the first-order derivatives, a new fourth-order compact difference (CD) scheme is constructed to solve the two-dimensional (2D) linear elliptic equation a mixed derivative. In this new scheme, unknown function and its first-order derivatives are regarded as the unknown variables in calculation. Then, the method is extended to solve the 2D parabolic equation with a mixed derivative. To match the spatial fourth-order accuracy, The backward differentiation formula (BDF) is employed to gain the fourth-order accuracy for the temporal discretization. Truncation error is analyzed to display that the present scheme is fourth-order accuracy in space. In order to solve the resulting large-scale linear equations, a multigrid method is employed to accelerate the convergence speed of the conventional relaxation methods. Finally, numerical results indicate that the present schemes obtain fourth-order convergence and are more accurate than those in the literature.
{"title":"High-order compact difference method for two-dimension elliptic and parabolic equations with mixed derivatives","authors":"Tingfu Ma, Y. Ge","doi":"10.32513/tbilisi/1608606055","DOIUrl":"https://doi.org/10.32513/tbilisi/1608606055","url":null,"abstract":"In this article, firstly, based on Taylor series expansion and truncation error correction technology, combined with the fourth-order Pade schemes of the first-order derivatives, a new fourth-order compact difference (CD) scheme is constructed to solve the two-dimensional (2D) linear elliptic equation a mixed derivative. In this new scheme, unknown function and its first-order derivatives are regarded as the unknown variables in calculation. Then, the method is extended to solve the 2D parabolic equation with a mixed derivative. To match the spatial fourth-order accuracy, The backward differentiation formula (BDF) is employed to gain the fourth-order accuracy for the temporal discretization. Truncation error is analyzed to display that the present scheme is fourth-order accuracy in space. In order to solve the resulting large-scale linear equations, a multigrid method is employed to accelerate the convergence speed of the conventional relaxation methods. Finally, numerical results indicate that the present schemes obtain fourth-order convergence and are more accurate than those in the literature.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"13 1","pages":"141-167"},"PeriodicalIF":0.5,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49473217","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/1608606053
E. Pişkin, Zeynep Çalişir
In this work, we consider a logarithmic Petrovsky equation with strong damping with initial and boundary conditions in a bounded domain. Under suitable conditions, we prove decay of solutions. Also, we establish the blow up at infinite time of solutions.
{"title":"Decay and blow up at infinite time of solutions for a logarithmic Petrovsky equation","authors":"E. Pişkin, Zeynep Çalişir","doi":"10.32513/tbilisi/1608606053","DOIUrl":"https://doi.org/10.32513/tbilisi/1608606053","url":null,"abstract":"In this work, we consider a logarithmic Petrovsky equation with strong damping with initial and boundary conditions in a bounded domain. Under suitable conditions, we prove decay of solutions. Also, we establish the blow up at infinite time of solutions.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"13 1","pages":"113-127"},"PeriodicalIF":0.5,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42743335","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/1608606050
Samet Maldar, Yunus Atalan, Kadri Doğan
In this paper, we have defined hyperbolic type of some iteration methods. The new iteration has been investigated convergence for mappings satisfying certain condition in hyperbolic spaces. It has been proved that this iteration is equivalent in terms of convergence with another iteration method in the same spaces. The rate of convergence of these two iteration methods have been compared. We have investigated data dependence result using hyperbolic type iteration. Finally, we have given numerical examples about rate of convergence and data dependence.
{"title":"Comparison rate of convergence and data dependence for a new iteration method","authors":"Samet Maldar, Yunus Atalan, Kadri Doğan","doi":"10.32513/tbilisi/1608606050","DOIUrl":"https://doi.org/10.32513/tbilisi/1608606050","url":null,"abstract":"In this paper, we have defined hyperbolic type of some iteration methods. The new iteration has been investigated convergence for mappings satisfying certain condition in hyperbolic spaces. It has been proved that this iteration is equivalent in terms of convergence with another iteration method in the same spaces. The rate of convergence of these two iteration methods have been compared. We have investigated data dependence result using hyperbolic type iteration. Finally, we have given numerical examples about rate of convergence and data dependence.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"13 1","pages":"65-79"},"PeriodicalIF":0.5,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46796681","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/1608606049
Merve Kara, D. T. Tollu, Y. Yazlik
{"title":"Global behavior of two-dimensional difference equations system with two period coefficients","authors":"Merve Kara, D. T. Tollu, Y. Yazlik","doi":"10.32513/tbilisi/1608606049","DOIUrl":"https://doi.org/10.32513/tbilisi/1608606049","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"13 1","pages":"49-64"},"PeriodicalIF":0.5,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46666632","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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