Pub Date : 2020-09-01DOI: 10.32513/tbilisi/1601344898
R. S. Dyavanal, Jyoti B. Muttagi, N. Shilpa
{"title":"Meromorphic solutions of some non-linear $q$-shift difference equations","authors":"R. S. Dyavanal, Jyoti B. Muttagi, N. Shilpa","doi":"10.32513/tbilisi/1601344898","DOIUrl":"https://doi.org/10.32513/tbilisi/1601344898","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"13 1","pages":"53-62"},"PeriodicalIF":0.5,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47722260","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 : 2020-07-03DOI: 10.32513/tbilisi/1608606048
Toshihiro Yamaguchi, Shoji Yokura
In this paper we introduce homological and homotopical Poincare polynomials $P_f(t)$ and $P^{pi}_f(t)$ of a continuous map $f:X to Y$ such that if $f:X to Y$ is a constant map, or more generally, if $Y$ is contractible, then these Poincare polynomials are respectively equal to the usual homological and homotopical Poincare polynomials $P_X(t)$ and $P^{pi}_X(t)$ of the source space $X$. Our relative Hilali conjecture $P^{pi}_f(1) leqq P_f(1)$ is a map version of the the well-known Hilali conjecture $P^{pi}_X(1) leqq P_X(1)$ of a rationally elliptic space X. In this paper we show that under the condition that $H_i(f;mathbb Q):H_i(X;mathbb Q) to H_i(Y;mathbb Q)$ is not injective for some $i>0$, the relative Hilali conjecture of product of maps holds, namely, there exists a positive integer $n_0$ such that for $forall n geqq n_0$ the emph{strict inequality $P^{pi}_{f^n}(1) < P_{f^n}(1)$} holds, where $f^n:X^n to Y^n$. In the final section we pose a question whether a "Hilali"-type inequality $HP^{pi}_X(r_X) leqq P_X(r_X)$ holds for a rationally hyperbolic space $X$, provided the the homotopical Hilbert--Poincare series $HP^{pi}_X(r_X)$ converges at the radius $r_X$ of convergence.
{"title":"Poincaré polynomials of a map and a relative Hilali conjecture","authors":"Toshihiro Yamaguchi, Shoji Yokura","doi":"10.32513/tbilisi/1608606048","DOIUrl":"https://doi.org/10.32513/tbilisi/1608606048","url":null,"abstract":"In this paper we introduce homological and homotopical Poincare polynomials $P_f(t)$ and $P^{pi}_f(t)$ of a continuous map $f:X to Y$ such that if $f:X to Y$ is a constant map, or more generally, if $Y$ is contractible, then these Poincare polynomials are respectively equal to the usual homological and homotopical Poincare polynomials $P_X(t)$ and $P^{pi}_X(t)$ of the source space $X$. Our relative Hilali conjecture $P^{pi}_f(1) leqq P_f(1)$ is a map version of the the well-known Hilali conjecture $P^{pi}_X(1) leqq P_X(1)$ of a rationally elliptic space X. In this paper we show that under the condition that $H_i(f;mathbb Q):H_i(X;mathbb Q) to H_i(Y;mathbb Q)$ is not injective for some $i>0$, the relative Hilali conjecture of product of maps holds, namely, there exists a positive integer $n_0$ such that for $forall n geqq n_0$ the emph{strict inequality $P^{pi}_{f^n}(1) < P_{f^n}(1)$} holds, where $f^n:X^n to Y^n$. In the final section we pose a question whether a \"Hilali\"-type inequality $HP^{pi}_X(r_X) leqq P_X(r_X)$ holds for a rationally hyperbolic space $X$, provided the the homotopical Hilbert--Poincare series $HP^{pi}_X(r_X)$ converges at the radius $r_X$ of convergence.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47207871","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 : 2020-01-01DOI: 10.32513/tbilisi/1585015225
Z. Çakir, C. Aykol, D. Soylemez, A. Serbetci
{"title":"Approximation by trigonometric polynomials in weighted Morrey spaces","authors":"Z. Çakir, C. Aykol, D. Soylemez, A. Serbetci","doi":"10.32513/tbilisi/1585015225","DOIUrl":"https://doi.org/10.32513/tbilisi/1585015225","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"13 1","pages":"123-138"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69696754","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 : 2020-01-01DOI: 10.32513/tbilisi/1585015226
S. Yildiz
{"title":"Abstract versions of Korovkin theorems on modular spaces via statistical relative summation process for double sequences","authors":"S. Yildiz","doi":"10.32513/tbilisi/1585015226","DOIUrl":"https://doi.org/10.32513/tbilisi/1585015226","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"25 3 1","pages":"139-156"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69696758","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 : 2020-01-01DOI: 10.32513/tbilisi/1593223225
M. Berbiche, M. Terchi
In this work, we consider the Cauchy problem for a wave equations with frictional and displacement dependent damping terms with nonlinear memory in multi-dimensional space $mathbb{R}^{n}$, $ngeq 1$, we will prove the existence and uniqueness of the local solution and the nonexistence of global weak solutions theorems for any dimension space.
{"title":"On the nonexistence of global solutions for wave equations with double damping terms and nonlinear memory","authors":"M. Berbiche, M. Terchi","doi":"10.32513/tbilisi/1593223225","DOIUrl":"https://doi.org/10.32513/tbilisi/1593223225","url":null,"abstract":"In this work, we consider the Cauchy problem for a wave equations with frictional and displacement dependent damping terms with nonlinear memory in multi-dimensional space $mathbb{R}^{n}$, $ngeq 1$, we will prove the existence and uniqueness of the local solution and the nonexistence of global weak solutions theorems for any dimension space.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69696368","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 : 2020-01-01DOI: 10.32513/tbilisi/1593223218
A. Mir
{"title":"Growth estimates of derivatives of a polynomial","authors":"A. Mir","doi":"10.32513/tbilisi/1593223218","DOIUrl":"https://doi.org/10.32513/tbilisi/1593223218","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"13 1","pages":"27-37"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69696767","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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