Let R be a semiprime ring, U a square-closed Lie ideal of R and D : R R ! R a symmetric reverse bi-derivation and d be the trace of D: In the present paper, we shall prove that R commutative ring if any one of the following holds: i) d(U) = (0); ii)d(U) Z; iii)[d (x) ; y] 2 Z; iv)d(x)oy 2 Z; v)d ([x; y])[d(x); y] 2 Z; vi)d (x y)(d(x)y) 2 Z; vii)d ([x; y])d(x)y 2 Z viii)d (x y) [d(x); y] 2 Z; ix)d(x) y [d(y); x] 2 Z; x)d([x; y]) (d(x) y) [d(y); x] 2 Z xi)[d(x); y] [g(y); x] 2 Z; for all x; y 2 U; where G : R R ! R is symmetric reverse bi-derivations such that g is the trace of
设R是一个半素环，U是R和D的平方闭李理想:R R !R是对称逆双导，d是d的迹。本文证明R交换环的成立条件为:i) d(U) = (0);(二)Z d (U);Iii)[d (x)];y] 2 Z;iv)d(x) y 2z;v) d ([x;y]) [d (x);y] 2 Z;vi)d (x)y (d(x)y) 2z;(七)d ([x;y])d(x)y 2zviii)d(x)y [d(x);y] 2 Z;d(x) y [d(y);x] 2 Z;x) d ([x;(d(x) Y) [d(Y);[x] 2zxi)[d(x);y] [g (y);x] 2 Z;对于所有x;y 2 U;G: R R R !R是对称逆双导使得g是的迹
{"title":"SOME RESULTS ON LIE IDEALS WITH SYMMETRIC REVERSE BI-DERIVATIONS IN SEMIPRIME RINGS I","authors":"Emine Koc Sogutcu, Ö. Gölbasi","doi":"10.22190/FUMI200708023K","DOIUrl":"https://doi.org/10.22190/FUMI200708023K","url":null,"abstract":"Let R be a semiprime ring, U a square-closed Lie ideal of R and D : R R ! R a symmetric reverse bi-derivation and d be the trace of D: In the present paper, we shall prove that R commutative ring if any one of the following holds: i) d(U) = (0); ii)d(U) Z; iii)[d (x) ; y] 2 Z; iv)d(x)oy 2 Z; v)d ([x; y])[d(x); y] 2 Z; vi)d (x y)(d(x)y) 2 Z; vii)d ([x; y])d(x)y 2 Z viii)d (x y) [d(x); y] 2 Z; ix)d(x) y [d(y); x] 2 Z; x)d([x; y]) (d(x) y) [d(y); x] 2 Z xi)[d(x); y] [g(y); x] 2 Z; for all x; y 2 U; where G : R R ! R is symmetric reverse bi-derivations such that g is the trace of","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82830748","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}
The aim of this paper is to introduce the absolute series space $leftvert mathcal{L}^{phi }(r,s)rightvert (mu )$ as the the set of all series summable by the absolute Lucas method, and to give its topological and algebraic structure such as $FK-$space, duals and Schauder basis. Also, certain matrix operators on this space are characterized.
{"title":"PARANORMED SPACES OF ABSOLUTE LUCAS SUMMABLE SERIES AND MATRIX OPERATORS","authors":"Fadime Gökçe","doi":"10.22190/FUMI200602020G","DOIUrl":"https://doi.org/10.22190/FUMI200602020G","url":null,"abstract":"The aim of this paper is to introduce the absolute series space $leftvert mathcal{L}^{phi }(r,s)rightvert (mu )$ as the the set of all series summable by the absolute Lucas method, and to give its topological and algebraic structure such as $FK-$space, duals and Schauder basis. Also, certain matrix operators on this space are characterized.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"15 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76261398","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}
The objective of present research article is to investigate the geometric properties of $eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds. In this manner, we consider $eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds satisfying $Rcdot S=0$. Further, we obtain results for $eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds with quasi-conformally flat property. Moreover, we get results for $eta$-Ricci solitons in Lorentzian para-Kenmotsu manifolds admitting Codazzi type of Ricci tensor and cyclic parallel Ricci tensor, $eta$-quasi-conformally semi-symmetric, $eta$-Ricci symmetric and quasi-conformally Ricci semi-symmetric. At last, we construct an example of a such manifold which justify the existence of proper $eta$-Ricci solitons.
{"title":"ETA-RICCI SOLITONS ON LORENTZIAN PARA-KENMOTSU MANIFOLDS","authors":"S. Pandey, Abhishek Singh, V. Mishra","doi":"10.22190/FUMI200923031P","DOIUrl":"https://doi.org/10.22190/FUMI200923031P","url":null,"abstract":"The objective of present research article is to investigate the geometric properties of $eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds. In this manner, we consider $eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds satisfying $Rcdot S=0$. Further, we obtain results for $eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds with quasi-conformally flat property. Moreover, we get results for $eta$-Ricci solitons in Lorentzian para-Kenmotsu manifolds admitting Codazzi type of Ricci tensor and cyclic parallel Ricci tensor, $eta$-quasi-conformally semi-symmetric, $eta$-Ricci symmetric and quasi-conformally Ricci semi-symmetric. At last, we construct an example of a such manifold which justify the existence of proper $eta$-Ricci solitons.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"123 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85265751","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}
In this paper, we introduce generalized (alpha, psi,phi)-contractive maps and provethe existence and uniqueness of xed points in complete S-metric spaces. We alsoprove that these maps satisfy property (P). We discuss the importance of study of the existence of xed points in S-metric space rather than in the setting of metric space.The results presented in this paper extends several well known comparable results in metric and G-metric spaces. We provide example in support of our result.
{"title":"FIXED POINTS OF GENERALIZED (ALPHA, PSI,PHI)-CONTRACTIVE MAPS AND PROPERTY(P) IN S-METRIC SPACES","authors":"G. Babu, Leta Bekere Kumssa","doi":"10.22190/FUMI200730026B","DOIUrl":"https://doi.org/10.22190/FUMI200730026B","url":null,"abstract":"In this paper, we introduce generalized (alpha, psi,phi)-contractive maps and provethe existence and uniqueness of xed points in complete S-metric spaces. We alsoprove that these maps satisfy property (P). We discuss the importance of study of the existence of xed points in S-metric space rather than in the setting of metric space.The results presented in this paper extends several well known comparable results in metric and G-metric spaces. We provide example in support of our result.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"3 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88782092","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}
In this present paper, we study an approximation properties of modified Baskakov-Gamma operator. Using Korovkin type theorem we first give approximation properties of this operator. Secondly, we compute the rate of convergence of this operator by means of the modulus of continuity and we give an approximation properties of weighted spaces. Finally, we study the Voronovskaya type theorem of this operator.
{"title":"APPROXIMATION PROPERTIES OF MODIFIED BASKAKOV GAMMA OPERATORS","authors":"Seda Arpagus, A. Olgun","doi":"10.22190/FUMI200325011A","DOIUrl":"https://doi.org/10.22190/FUMI200325011A","url":null,"abstract":"In this present paper, we study an approximation properties of modified Baskakov-Gamma operator. Using Korovkin type theorem we first give approximation properties of this operator. Secondly, we compute the rate of convergence of this operator by means of the modulus of continuity and we give an approximation properties of weighted spaces. Finally, we study the Voronovskaya type theorem of this operator.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"29 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72816914","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}
In this paper, we introduce the concepts of ideal ∆α−lacunary statis- tical convergence of order β with the fractional order of α and ideal ∆α−lacunary strongly convergence of order β with the fractional order of α ( where 0 < β ≤ 1and α be a fractional order) and give some relations about these concepts.
{"title":"I−LACUNARY STATISTICAL CONVERGENCE OF ORDER β OF DIFFERENCE SEQUENCES OF FRACTIONAL ORDER","authors":"N. D. Aral, H. Kandemir","doi":"10.22190/FUMI200117004A","DOIUrl":"https://doi.org/10.22190/FUMI200117004A","url":null,"abstract":"In this paper, we introduce the concepts of ideal ∆α−lacunary statis- tical convergence of order β with the fractional order of α and ideal ∆α−lacunary strongly convergence of order β with the fractional order of α ( where 0 < β ≤ 1and α be a fractional order) and give some relations about these concepts.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"102 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80574819","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}
Let A, A_{1}, A_{2}, B, B_{1}, B_{2}, C_{1} and C_{2} be linear bounded operators on Hilbert spaces. In this paper, by using generalized inverses, we establish necessary and sufficient conditions for the existence of a common solution and give the form of the general common solution of the operator equations A_{1}XB_{1}=C_{1} and A_{2}XB_{2}=C_{2}, we apply this result to determine new necessary and sufficient conditions for the existence of Hermitian solutions and give the form of the general Hermitian solution to the operator equation AXB=C. As a consequence, we give necessary and sufficient condition for the existence of Hermitian solution to the operator equation AXA^{*}+BYB^{*}=C.
{"title":"HERIMITIAN SOLUTIONS TO THE EQUATION AXA* + BYB* = C, FOR HILBERT SPACE OPERATORS","authors":"Amina Boussaid, F. Lombarkia","doi":"10.22190/FUMI191108001B","DOIUrl":"https://doi.org/10.22190/FUMI191108001B","url":null,"abstract":"Let A, A_{1}, A_{2}, B, B_{1}, B_{2}, C_{1} and C_{2} be linear bounded operators on Hilbert spaces. In this paper, by using generalized inverses, we establish necessary and sufficient conditions for the existence of a common solution and give the form of the general common solution of the operator equations A_{1}XB_{1}=C_{1} and A_{2}XB_{2}=C_{2}, we apply this result to determine new necessary and sufficient conditions for the existence of Hermitian solutions and give the form of the general Hermitian solution to the operator equation AXB=C. As a consequence, we give necessary and sufficient condition for the existence of Hermitian solution to the operator equation AXA^{*}+BYB^{*}=C.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"28 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83422011","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}
The rapid development of digital computer hardware and software has had a dramatic influence on mathematics, and contrary. The advanced hardware and modern sophistical software such as computer visualization, symbolic computation, computerassisted proofs, multi-precision arithmetic and powerful libraries, have provided resolving many open problems, a huge very difficult mathematical problems, and discovering new patterns and relationships, far beyond a human capability. In the first part of the paper we give a short review of some typical mathematical problems solved by computer tools. In the second part we present some new original contributions, such as intriguing consequence of the presence of roundoff errors, distribution of zeros of random polynomials, dynamic study of zero-finding methods, a new three-point family of methods for solving nonlinear equations and two algorithms for the inclusion of a simple complex zero of a polynomial.
{"title":"COMPUTER TOOLS FOR SOLVING MATHEMATICAL PROBLEMS: A REVIEW","authors":"I. Petkovic, Đ. Herceg","doi":"10.22190/FUMI201203017P","DOIUrl":"https://doi.org/10.22190/FUMI201203017P","url":null,"abstract":"The rapid development of digital computer hardware and software has had a dramatic influence on mathematics, and contrary. The advanced hardware and modern sophistical software such as computer visualization, symbolic computation, computerassisted proofs, multi-precision arithmetic and powerful libraries, have provided resolving many open problems, a huge very difficult mathematical problems, and discovering new patterns and relationships, far beyond a human capability. In the first part of the paper we give a short review of some typical mathematical problems solved by computer tools. In the second part we present some new original contributions, such as intriguing consequence of the presence of roundoff errors, distribution of zeros of random polynomials, dynamic study of zero-finding methods, a new three-point family of methods for solving nonlinear equations and two algorithms for the inclusion of a simple complex zero of a polynomial.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"24 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82800166","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}
In this paper, we introduce a new sequential space as a generalization of M − metricspaces and M b − metric spaces. In this generalized space we define two contractive mappings namely m − contraction and m − quasi-contraction and prove some fixed point theorems for such type of mappings. Several illustrative examples have been presented in strengthening the hypothesis of our theorems.
{"title":"A NEW GENERALIZATION OF M-METRIC SPACE WITH SOME FIXED POINT THEOREMS","authors":"E. Karapınar, K. Roy, M. Saha","doi":"10.22190/FUMI200310007K","DOIUrl":"https://doi.org/10.22190/FUMI200310007K","url":null,"abstract":"In this paper, we introduce a new sequential space as a generalization of M − metricspaces and M b − metric spaces. In this generalized space we define two contractive mappings namely m − contraction and m − quasi-contraction and prove some fixed point theorems for such type of mappings. Several illustrative examples have been presented in strengthening the hypothesis of our theorems.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73355495","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}
In this paper, we introduce the concept of triangular A-statistical relative convergence for double sequences of functions defined on a compactsubset of the real two-dimensional space. Based upon this new convergencemethod, we prove Korovkin-type approximation theorem. Finally, we give some further developments.
{"title":"TRIANGULAR A−STATISTICAL RELATIVE UNIFORM CONVERGENCE FOR DOUBLE SEQUENCES OF POSITIVE LINEAR OPERATORS","authors":"Selin Çınar","doi":"10.22190/FUMI200309006C","DOIUrl":"https://doi.org/10.22190/FUMI200309006C","url":null,"abstract":"In this paper, we introduce the concept of triangular A-statistical relative convergence for double sequences of functions defined on a compactsubset of the real two-dimensional space. Based upon this new convergencemethod, we prove Korovkin-type approximation theorem. Finally, we give some further developments.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89494298","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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