In this paper, we determine some properties of extended eigenvalues for operators pair. Furthermore, the relationship between this kind of operators pair and the operators pencils in Hilbert space is established.
{"title":"Some properties of extended eigenvalues for operators pair","authors":"A. Ammar, Chaimaa Bouchama, A. Jeribi","doi":"10.2298/fil2306927a","DOIUrl":"https://doi.org/10.2298/fil2306927a","url":null,"abstract":"In this paper, we determine some properties of extended eigenvalues for operators pair. Furthermore, the relationship between this kind of operators pair and the operators pencils in Hilbert space is established.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68271272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A Roman domination function (RDF) on a graph G with a set of vertices V = V(G) is a function f : V ? {0, 1, 2} which satisfies the condition that each vertex v ? V such that f (v) = 0 is adjacent to at least one vertex u such that f (u) = 2. The minimum weight value of an RDF on graph G is called the Roman domination number (RDN) of G and it is denoted by ?R(G). An RDF for which ?R(G) is achieved is called a ?R(G)-function. This paper considers Roman domination problem for Johnson graphs Jn,2 and Jn,3. For Jn,2, n ? 4 it is proved that ?R(Jn,2) = n ? 1. New lower and upper bounds for Jn,3, n ? 6 are derived using results on the minimal coverings of pairs by triples. These bounds quadratically depend on dimension n.
具有一组顶点V = V(G)的图G上的罗马支配函数(RDF)是函数f: V ?{0,1,2}满足每个顶点v ?使得f (V) = 0的V与至少一个顶点u相邻使得f (u) = 2。图G上RDF的最小权值称为图G的罗马支配数(RDN)，用?R(G)表示。实现R(G)的RDF称为R(G)函数。本文研究了Johnson图Jn,2和Jn,3的罗马支配问题。对于Jn,2, n ?证明了?R(Jn,2) = n ?1. 新的Jn 3 n的下界和上界?6是由三元组对的最小覆盖的结果导出的。这些边界二次依赖于维数n。
{"title":"On the Roman domination problem of some Johnson graphs","authors":"Tatjana Zec","doi":"10.2298/fil2307067z","DOIUrl":"https://doi.org/10.2298/fil2307067z","url":null,"abstract":"A Roman domination function (RDF) on a graph G with a set of vertices V = V(G) is a function f : V ? {0, 1, 2} which satisfies the condition that each vertex v ? V such that f (v) = 0 is adjacent to at least one vertex u such that f (u) = 2. The minimum weight value of an RDF on graph G is called the Roman domination number (RDN) of G and it is denoted by ?R(G). An RDF for which ?R(G) is achieved is called a ?R(G)-function. This paper considers Roman domination problem for Johnson graphs Jn,2 and Jn,3. For Jn,2, n ? 4 it is proved that ?R(Jn,2) = n ? 1. New lower and upper bounds for Jn,3, n ? 6 are derived using results on the minimal coverings of pairs by triples. These bounds quadratically depend on dimension n.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68271302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we consider a class of weighted composition operators defined on the weighted Bergman spaces L2a (dA?) where D is the open unit disk in C and dA?(z) = (? + 1)(1 ? |z|2)?dA(z), ? > ?1 and dA(z) is the area measure on D. These operators are also self-adjoint and unitary. We establish here that a bounded linear operator S from L2a (dA?) into itself commutes with all the composition operators C(?) a , a ? D, if and only if B?S satisfies certain averaging condition. Here B?S denotes the generalized Berezin transform of the bounded linear operator S from L2a (dA?) into itself, C(?) a f = ( f ??a), f ? L2a (dA?) and ? ? Aut(D). Applications of the result are also discussed. Further, we have shown that ifMis a subspace of L?(D) and if for ? ? M, the Toeplitz operator T(?) ? represents a multiplication operator on a closed subspace S ? L2a (dA?), then ? is bounded analytic on D. Similarly if q ? L?(D) and Bn is a finite Blaschke product and M(?) q ( Range C(?) Bn) ? L2a (dA?), then q ? H?(D). Further, we have shown that if ? ? Aut(D), then N = {q ? L2a (dA?) : M(?) q (Range C(?)?) ? L2a (dA?)} = H?(D) if and only if ? is a finite Blaschke product. Here M(?)?, T(?)? , C(?)? denote the multiplication operator, the Toeplitz operator and the composition operator defined on L2a (dA?) with symbol ? respectively.
在本文中，我们考虑了一类定义在加权Bergman空间L2a (dA?)上的加权复合算子，其中D是C中的开放单位盘，dA?(z) = (?)+ 1 (1 ?| | 2 z) ? dA (z) ?> ?1, dA(z)是d上的面积测度，这些算子也是自伴随的酉算子。我们在这里建立一个有界线性算子S从L2a (dA?)到它自身与所有复合算子C(?) a a ?D，当且仅当B?S满足一定的平均条件。B ?S表示有界线性算子S从L2a (dA?)到自身的广义Berezin变换，C(?) a f = (f ?a)， f ?L2a (dA?)和?？ Aut (D)。并对结果的应用进行了讨论。进一步，我们证明了if是L?(D)的一个子空间，如果为?？ M, Toeplitz算子T(?) ?表示闭子空间S上的乘法算子?L2a (dA?)在d上是有界解析的，同理，如果q ?L?(D)和Bn是有限Blaschke积，M(?) q(范围C(?))Bn) ?L2a (dA?)，然后q ?H ? (D)。此外，我们已经证明，如果?？ Aut(D)，则N = {q ?L2a (dA?): M(?) q(范围C(?)?) ?L2a (dA?)} = H?(D)当且仅当?是有限Blaschke积。这里M (?) ?T(?)吗?C(?)吗?用符号?表示在L2a (dA?)上定义的乘法运算符、Toeplitz运算符和复合运算符。分别。
{"title":"On a class of unitary operators on weighted Bergman spaces","authors":"N. Das, Swarupa Roy","doi":"10.2298/fil2307013d","DOIUrl":"https://doi.org/10.2298/fil2307013d","url":null,"abstract":"In this paper we consider a class of weighted composition operators defined on the weighted Bergman spaces L2a (dA?) where D is the open unit disk in C and dA?(z) = (? + 1)(1 ? |z|2)?dA(z), ? > ?1 and dA(z) is the area measure on D. These operators are also self-adjoint and unitary. We establish here that a bounded linear operator S from L2a (dA?) into itself commutes with all the composition operators C(?) a , a ? D, if and only if B?S satisfies certain averaging condition. Here B?S denotes the generalized Berezin transform of the bounded linear operator S from L2a (dA?) into itself, C(?) a f = ( f ??a), f ? L2a (dA?) and ? ? Aut(D). Applications of the result are also discussed. Further, we have shown that ifMis a subspace of L?(D) and if for ? ? M, the Toeplitz operator T(?) ? represents a multiplication operator on a closed subspace S ? L2a (dA?), then ? is bounded analytic on D. Similarly if q ? L?(D) and Bn is a finite Blaschke product and M(?) q ( Range C(?) Bn) ? L2a (dA?), then q ? H?(D). Further, we have shown that if ? ? Aut(D), then N = {q ? L2a (dA?) : M(?) q (Range C(?)?) ? L2a (dA?)} = H?(D) if and only if ? is a finite Blaschke product. Here M(?)?, T(?)? , C(?)? denote the multiplication operator, the Toeplitz operator and the composition operator defined on L2a (dA?) with symbol ? respectively.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68271506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we obtain an existence result for the integral boundary value problems of nonlinear fractional q-difference equations on the half-line using Schauder?s fixed point theorem.
本文利用Schauder?S不动点定理。
{"title":"Existence result for fractional q-difference equations on the half-line","authors":"Öyküm Ülke, F. Topal","doi":"10.2298/fil2305591u","DOIUrl":"https://doi.org/10.2298/fil2305591u","url":null,"abstract":"In this paper, we obtain an existence result for the integral boundary value problems of nonlinear fractional q-difference equations on the half-line using Schauder?s fixed point theorem.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68270635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper deals with the characterization of compact operators on Ces?ro sequence spaces as an application of Hausdorff measure of noncompactness. Further, the norms of Ces?ro operators on certain spaces are investigated.
{"title":"Compact operators on Cesàro sequence spaces and norms of Cesàro operators","authors":"Merve İlkhan Kara, H. Roopaei","doi":"10.2298/fil2305673i","DOIUrl":"https://doi.org/10.2298/fil2305673i","url":null,"abstract":"This paper deals with the characterization of compact operators on Ces?ro sequence spaces as an application of Hausdorff measure of noncompactness. Further, the norms of Ces?ro operators on certain spaces are investigated.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68270678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper deals with on the continuity of the solution to the Minkowski problem for Lp torsional measure. For p ? (1, n + 2) ? (n + 2,?), we show that a sequence of convex bodies in Rn is convergent in Hausdorff metric if the sequence of the Lp torsional measures (associated with these convex bodies) is weakly convergent. Moreover, we also prove that the solution to the Minkowski problem for Lp torsional measure is continuous with respect to p.
本文讨论了Lp扭转测度Minkowski问题解的连续性问题。对于p ?(1, n + 2) ?(n + 2，?)，我们证明了如果(与这些凸体相关的)Lp扭转测度序列弱收敛，则Rn中的凸体序列在Hausdorff度量中收敛。此外，我们还证明了Lp扭转测度Minkowski问题的解相对于p是连续的。
{"title":"On the continuity of the solution to the Minkowski problem for Lp torsional measure","authors":"Ni Li, Shuang Mou","doi":"10.2298/fil2308387l","DOIUrl":"https://doi.org/10.2298/fil2308387l","url":null,"abstract":"This paper deals with on the continuity of the solution to the Minkowski problem for Lp torsional measure. For p ? (1, n + 2) ? (n + 2,?), we show that a sequence of convex bodies in Rn is convergent in Hausdorff metric if the sequence of the Lp torsional measures (associated with these convex bodies) is weakly convergent. Moreover, we also prove that the solution to the Minkowski problem for Lp torsional measure is continuous with respect to p.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68272745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the approximate biprojectivity and the approximate biflatness of a Banach algebra A and find some relations between theses concepts with ?-amenability and ? -contractibility, where ? is a character on A. Among other things, we show that ?-Lau product algebra L1(G) ?? A(G) is approximately biprojective if and only if G is finite, where L1(G) and A(G) are the group algebra and the Fourier algebra of a locally compact group G, respectively. We also characterize approximately biprojective and approximately biflat semigroup algebras associated with the inverse semigroups.
{"title":"On approximately biprojective and approximately biflat Banach algebras","authors":"A. Sahami, A. Bodaghi","doi":"10.2298/fil2308295s","DOIUrl":"https://doi.org/10.2298/fil2308295s","url":null,"abstract":"In this paper, we study the approximate biprojectivity and the approximate biflatness of a Banach algebra A and find some relations between theses concepts with ?-amenability and ? -contractibility, where ? is a character on A. Among other things, we show that ?-Lau product algebra L1(G) ?? A(G) is approximately biprojective if and only if G is finite, where L1(G) and A(G) are the group algebra and the Fourier algebra of a locally compact group G, respectively. We also characterize approximately biprojective and approximately biflat semigroup algebras associated with the inverse semigroups.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68272822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the present paper we introduce and study some lacunary difference bicomplex sequence spaces by means of Orlicz functions. We make an effort to study some algebraic and topological properties of these sequence spaces. We also show that these spaces are complete paranormed spaces. Further, some inclusion relations between these spaces and some interesting examples are established. Finally, we prove some results on modified complex Banach Algebra in the third section of the paper.
{"title":"Orlicz-Lacunary bicomplex sequence spaces of difference operators","authors":"K. Raj, A. Esi, C. Sharma","doi":"10.2298/fil2308421r","DOIUrl":"https://doi.org/10.2298/fil2308421r","url":null,"abstract":"In the present paper we introduce and study some lacunary difference bicomplex sequence spaces by means of Orlicz functions. We make an effort to study some algebraic and topological properties of these sequence spaces. We also show that these spaces are complete paranormed spaces. Further, some inclusion relations between these spaces and some interesting examples are established. Finally, we prove some results on modified complex Banach Algebra in the third section of the paper.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68272916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper intends to show some operator and norm inequalities involving synchronous and asynchronous functions. Among other inequalities, it is shown that if A, B ? B(H) are two positive operators and f,g: J ? R are asynchronous functions, then f(A)g(A) + f(B)g(B) ? 1/2(f2(A)+12 (A) + f2(B)+g2(B)).
本文给出了同步函数和异步函数的算子和范数不等式。在其他不等式中，它表明如果A, B ?B(H)是两个正算子f,g: J ?R是异步函数，那么f(A)g(A) + f(B)g(B) ?1/2(f2(A)+12 (A)+ f2(B)+g2(B))
{"title":"Further inequalities related to synchronous and asynchronous functions","authors":"Mahdi Ghasvareh, M. Omidvar","doi":"10.2298/fil2308599g","DOIUrl":"https://doi.org/10.2298/fil2308599g","url":null,"abstract":"This paper intends to show some operator and norm inequalities involving synchronous and asynchronous functions. Among other inequalities, it is shown that if A, B ? B(H) are two positive operators and f,g: J ? R are asynchronous functions, then f(A)g(A) + f(B)g(B) ? 1/2(f2(A)+12 (A) + f2(B)+g2(B)).","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68275312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study relative controllability of linear and nonlinear conformable delay differential systems with linear parts defined by permutable matrices. By using a notion of delay Grammian matrix, we give a sufficient and necessary condition to examine that a linear delay controlled systems is relatively controllable. Thereafter, we construct a suitable control function for nonlinear delay controlled system, which admits us to adopt the framework of fixed point methods to investigate the same issue. More precisely, we apply Krassnoselskii?s fixed point theorem to derive a relative controllability result. Finally, two examples are presented to illustrate our theoretical results with the help of computing the desired control functions and inverse of delay Grammian matrix as well.
{"title":"Relative controllability of conformable delay differential systems with linear parts defined by permutable matrices","authors":"Airen Zhou, Jinrong Wang","doi":"10.2298/fil2309659z","DOIUrl":"https://doi.org/10.2298/fil2309659z","url":null,"abstract":"We study relative controllability of linear and nonlinear conformable delay differential systems with linear parts defined by permutable matrices. By using a notion of delay Grammian matrix, we give a sufficient and necessary condition to examine that a linear delay controlled systems is relatively controllable. Thereafter, we construct a suitable control function for nonlinear delay controlled system, which admits us to adopt the framework of fixed point methods to investigate the same issue. More precisely, we apply Krassnoselskii?s fixed point theorem to derive a relative controllability result. Finally, two examples are presented to illustrate our theoretical results with the help of computing the desired control functions and inverse of delay Grammian matrix as well.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135783581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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