Pub Date : 2021-06-01DOI: 10.32513/tmj/19322008119
Chao Meng, Gang Liu
In this paper, we study the value sharing problems for certain types of difference polynomials with the notion of weakly weighted sharing. Our results improve and generalize the results due to P. Sahoo and B. Saha [App. Math. E-Notes. 16(2016), 33-44], H.P. Waghamore [Tbilisi Math. J. 11(2018), 1-13].
{"title":"Value sharing problems for certain types of difference polynomials","authors":"Chao Meng, Gang Liu","doi":"10.32513/tmj/19322008119","DOIUrl":"https://doi.org/10.32513/tmj/19322008119","url":null,"abstract":"In this paper, we study the value sharing problems for certain types of difference polynomials with the notion of weakly weighted sharing. Our results improve and generalize the results due to P. Sahoo and B. Saha [App. Math. E-Notes. 16(2016), 33-44], H.P. Waghamore [Tbilisi Math. J. 11(2018), 1-13].","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":"41879365","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/19322008130
T. Usman, R. Khan, M. Aman, Y. Gasimov
In this paper, we introduce a new class of Legendre poly-Genocchi polynomials and give some identities of these polynomials related to the Stirling numbers of the second kind. The concept of poly-Bernoulli numbers $B_{n}^{(k)}(a,b)$, poly-Bernoulli polynomials $B_{n}^{(k)}(x,a,b)$ of Jolany et al., Hermite-Bernoulli polynomials ${}_{H}B_{n}(x,y)$ of Dattoli et al., ${}_{H}B_{n}^{(alpha)}(x,y)$ of Pathan et al. and ${}_{H}G_{n}^{(k)}(x,y)$ of Khan are generalized to the one $_{S}G_{n}^{(k)}(x,y,z)$. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating function. These results extended some known summation and identities of Hermite poly-Genocchi numbers and polynomials.
{"title":"A unified family of multivariable Legendre poly-Genocchi polynomials","authors":"T. Usman, R. Khan, M. Aman, Y. Gasimov","doi":"10.32513/tmj/19322008130","DOIUrl":"https://doi.org/10.32513/tmj/19322008130","url":null,"abstract":"In this paper, we introduce a new class of Legendre poly-Genocchi polynomials and give some identities of these polynomials related to the Stirling numbers of the second kind. The concept of poly-Bernoulli numbers $B_{n}^{(k)}(a,b)$, poly-Bernoulli polynomials $B_{n}^{(k)}(x,a,b)$ of Jolany et al., Hermite-Bernoulli polynomials ${}_{H}B_{n}(x,y)$ of Dattoli et al., ${}_{H}B_{n}^{(alpha)}(x,y)$ of Pathan et al. and ${}_{H}G_{n}^{(k)}(x,y)$ of Khan are generalized to the one $_{S}G_{n}^{(k)}(x,y,z)$. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating function. These results extended some known summation and identities of Hermite poly-Genocchi numbers and polynomials.","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":"41882986","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/19322008132
A. Mammadova, A. Abdullayeva
In the present paper we consider the generalized Bernstein-Chlodowsky polynomial and two variable generalized Szasz operator. For the first operator we obtain convergence property on bounded intervals of positive semi-axis. For the second operator, we obtain direct approximation property on positive semi-axis as estimate of the two variable generalized Szasz operator by two variable weighted modulus of continuity.
{"title":"Approximation properties of generalized Szasz and Bernstein-Chlodowsky operators","authors":"A. Mammadova, A. Abdullayeva","doi":"10.32513/tmj/19322008132","DOIUrl":"https://doi.org/10.32513/tmj/19322008132","url":null,"abstract":"In the present paper we consider the generalized Bernstein-Chlodowsky polynomial and two variable generalized Szasz operator. For the first operator we obtain convergence property on bounded intervals of positive semi-axis. For the second operator, we obtain direct approximation property on positive semi-axis as estimate of the two variable generalized Szasz operator by two variable weighted modulus of continuity.","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":"48137522","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/19322008121
Yu Miao
In the present paper, by virtue of probability approach, we study an open problem which was proposed by " F. Qi, Several integral inequalities, J. Inequal. Pure Appl. Math. 1 (2000), no. 2, Art. 19; available online at {http://emis.icm.edu.pl/journals/JIPAM/article113.html?sid=113}.", and obtain several generalized Qi-type inequalities which extend and improve some known results.
{"title":"Some generalized Qi-type inequalities","authors":"Yu Miao","doi":"10.32513/tmj/19322008121","DOIUrl":"https://doi.org/10.32513/tmj/19322008121","url":null,"abstract":"In the present paper, by virtue of probability approach, we study an open problem which was proposed by \" F. Qi, Several integral inequalities, J. Inequal. Pure Appl. Math. 1 (2000), no. 2, Art. 19; available online at {http://emis.icm.edu.pl/journals/JIPAM/article113.html?sid=113}.\", and obtain several generalized Qi-type inequalities which extend and improve some known results.","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":"44710884","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/19322008131
Zehra Pinar
In this work, we consider that the two-mode equations, especially two-mode Korteweg-de Vries equation and two-mode Sharma-Tasso-Olver equations, which are used for modelling of shallow water waves, electromagnetism, electrical and electronics engineering, signal analysis, quantum mechanics etc. and their analytical solutions are obtained via the well-known Bernoulli equation method through the symbolic computation.
{"title":"On the wave solutions of two-mode equations","authors":"Zehra Pinar","doi":"10.32513/tmj/19322008131","DOIUrl":"https://doi.org/10.32513/tmj/19322008131","url":null,"abstract":"In this work, we consider that the two-mode equations, especially two-mode Korteweg-de Vries equation and two-mode Sharma-Tasso-Olver equations, which are used for modelling of shallow water waves, electromagnetism, electrical and electronics engineering, signal analysis, quantum mechanics etc. and their analytical solutions are obtained via the well-known Bernoulli equation method through the symbolic computation.","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":"47426310","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/19322008129
Vildan Ozturk
In this paper we introduce $zeta -$contraction via simulation function in uniform spaces and prove new fixed point theorem for $zeta-$contraction in uniform spaces.
{"title":"Fixed point theorems for $zeta-$contractions in uniform spaces","authors":"Vildan Ozturk","doi":"10.32513/tmj/19322008129","DOIUrl":"https://doi.org/10.32513/tmj/19322008129","url":null,"abstract":"In this paper we introduce $zeta -$contraction via simulation function in uniform spaces and prove new fixed point theorem for $zeta-$contraction in uniform spaces.","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":"42816282","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/19322008122
Morteza Kardel, R. Sanati
In this paper, introducing the notion of topologically simple pro $C^*$-algebras, we show that direct product of $C^*$-algebras $K(H_i)$, as the set of all compact operators on a Hilbert space $H_i$, is a topologically simple pro $C^*$-algebra. Applying this fact, we prove that the set of all bounded elements of a certain class of Hilbert modules are dense in the same module.
{"title":"A certain class of pro $C^*$-algebras and bounded elements of a Hilbert module","authors":"Morteza Kardel, R. Sanati","doi":"10.32513/tmj/19322008122","DOIUrl":"https://doi.org/10.32513/tmj/19322008122","url":null,"abstract":"In this paper, introducing the notion of topologically simple pro $C^*$-algebras, we show that direct product of $C^*$-algebras $K(H_i)$, as the set of all compact operators on a Hilbert space $H_i$, is a topologically simple pro $C^*$-algebra. Applying this fact, we prove that the set of all bounded elements of a certain class of Hilbert modules are dense in the same module.","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":"44394930","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/19322008126
F. Erduvan, R. Keskin
In this paper, we find all Fibonacci numbers which are products of two Jacobsthal numbers. Also we find all Jacobsthal numbers which are products of two Fibonacci numbers. More generally, taking $k,m,n$ as positive integers, it is proved that $F_{k}=J_{m}J_{n}$ implies that begin{align*} (k,m,n) = &(1,1,1),(2,1,1),(1,1,2),(2,1,2), & (1,2,2),(2,2,2),(4,1,3),(4,2,3), & (5,1,4),(5,2,4),(10,4,5),(8,1,6),(8,2,6) end{align*} and $J_{k}=F_{m}F_{n}$ implies that begin{align*} (k,m,n) =&(1,1,1),(2,1,1),(1,2,1),(2,2,1), & (1,2,2),(2,2,2),(3,4,1),(3,4,2), & (4,5,1),(4,5,2),(6,8,1),(6,8,2). end{align*}
{"title":"Fibonacci numbers which are products of two Jacobsthal numbers","authors":"F. Erduvan, R. Keskin","doi":"10.32513/tmj/19322008126","DOIUrl":"https://doi.org/10.32513/tmj/19322008126","url":null,"abstract":"In this paper, we find all Fibonacci numbers which are products of two Jacobsthal numbers. Also we find all Jacobsthal numbers which are products of two Fibonacci numbers. More generally, taking $k,m,n$ as positive integers, it is proved that $F_{k}=J_{m}J_{n}$ implies that begin{align*} (k,m,n) = &(1,1,1),(2,1,1),(1,1,2),(2,1,2), & (1,2,2),(2,2,2),(4,1,3),(4,2,3), & (5,1,4),(5,2,4),(10,4,5),(8,1,6),(8,2,6) end{align*} and $J_{k}=F_{m}F_{n}$ implies that begin{align*} (k,m,n) =&(1,1,1),(2,1,1),(1,2,1),(2,2,1), & (1,2,2),(2,2,2),(3,4,1),(3,4,2), & (4,5,1),(4,5,2),(6,8,1),(6,8,2). end{align*}","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":"46372817","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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