In this article we are interested to give an analogue result of the subdifferentiation of the marginal functions in Banach spaces established by Mordukhovich and Shao in [6] using the so-called the srtong generalized limiting subdifferential defined in binormed space introduced by Hlal in [3]. AMS Subject Classification: 49J52, 49J50
{"title":"SOME APPLICATIONS OF NON CONVEX SUBDIFFERENTIAL CALCULUS IN BINORMED SPACES","authors":"J. Hlal","doi":"10.12732/ijam.v33i2.8","DOIUrl":"https://doi.org/10.12732/ijam.v33i2.8","url":null,"abstract":"In this article we are interested to give an analogue result of the subdifferentiation of the marginal functions in Banach spaces established by Mordukhovich and Shao in [6] using the so-called the srtong generalized limiting subdifferential defined in binormed space introduced by Hlal in [3]. AMS Subject Classification: 49J52, 49J50","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"1 1","pages":"297"},"PeriodicalIF":0.0,"publicationDate":"2020-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82237101","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}
Abstract: We address the question of expressing the sums of the powers of polygonal numbers in closed forms using some basic functions. We obtain explicit expressions for the closed form expressions for the sums of the squares of reciprocals of polygonal numbers, the sums of the cubes of reciprocals of polygonal numbers the sums of the fourth-powers of reciprocals of polygonal numbers. These closed form expressions are composed of digamma function, Riemann zeta function and the Hurwitz zeta function. It has been possible to obtain the general result for the sums of an arbitrary power of reciprocals of square numbers. An outline is given to extend the result to the general case of the sums of the powers of reciprocals of polygonal numbers.
{"title":"SUMS OF THE POWERS OF RECIPROCALS OF POLYGONAL NUMBERS","authors":"S. Khan","doi":"10.12732/ijam.v33i2.6","DOIUrl":"https://doi.org/10.12732/ijam.v33i2.6","url":null,"abstract":"Abstract: We address the question of expressing the sums of the powers of polygonal numbers in closed forms using some basic functions. We obtain explicit expressions for the closed form expressions for the sums of the squares of reciprocals of polygonal numbers, the sums of the cubes of reciprocals of polygonal numbers the sums of the fourth-powers of reciprocals of polygonal numbers. These closed form expressions are composed of digamma function, Riemann zeta function and the Hurwitz zeta function. It has been possible to obtain the general result for the sums of an arbitrary power of reciprocals of square numbers. An outline is given to extend the result to the general case of the sums of the powers of reciprocals of polygonal numbers.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"21 1","pages":"265"},"PeriodicalIF":0.0,"publicationDate":"2020-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85906451","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 concept of partial metric was initiated by Matthews [14] as a part of study of denotational semantics of flow networks. In fact, the partial metric plays a very important role in development of models in theory of computation and computer domain theory. In this paper we provide some common fixed point results by using generalized Caristi type contraction. AMS Subject Classification: 22E46, 53C35, 57S20
{"title":"SOME FIXED POINT RESULTS VIA GENERALIZED CARISTI CONTRACTIONS IN PARTIAL METRIC SPACES","authors":"D. R. Prasad, G. Kishore, V. Bhagavan","doi":"10.12732/ijam.v33i2.3","DOIUrl":"https://doi.org/10.12732/ijam.v33i2.3","url":null,"abstract":"The concept of partial metric was initiated by Matthews [14] as a part of study of denotational semantics of flow networks. In fact, the partial metric plays a very important role in development of models in theory of computation and computer domain theory. In this paper we provide some common fixed point results by using generalized Caristi type contraction. AMS Subject Classification: 22E46, 53C35, 57S20","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"98 1","pages":"225"},"PeriodicalIF":0.0,"publicationDate":"2020-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77025310","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":"A NORM INEQUALITY FOR FUNCTIONS OF $L^{pleft( .right) }left(Omega right)$ SPACES","authors":"Y. Kaya","doi":"10.12732/ijam.v33i2.10","DOIUrl":"https://doi.org/10.12732/ijam.v33i2.10","url":null,"abstract":"","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"41 1","pages":"313"},"PeriodicalIF":0.0,"publicationDate":"2020-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73859576","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 exponential stability concept for nonlinear non-instantaneous impulsive difference equations with a single delay is studied and some criteria are derived. These results are also applied for a neural networks with switching topology at certain moments and long time lasting impulses. It is considered the general case of time varying connection weights. The equilibrium is defined and exponential stability is studied. The obtained results are illustrated on examples. AMS Subject Classification: 39A30, 39A60
{"title":"EXPONENTIAL STABILITY OF DISCRETE NEURAL NETWORKS WITH NON-INSTANTANEOUS IMPULSES, DELAYS AND VARIABLE CONNECTION WEIGHTS WITH COMPUTER SIMULATION","authors":"S. Hristova, K. Stefanova","doi":"10.12732/ijam.v33i2.1","DOIUrl":"https://doi.org/10.12732/ijam.v33i2.1","url":null,"abstract":"The exponential stability concept for nonlinear non-instantaneous impulsive difference equations with a single delay is studied and some criteria are derived. These results are also applied for a neural networks with switching topology at certain moments and long time lasting impulses. It is considered the general case of time varying connection weights. The equilibrium is defined and exponential stability is studied. The obtained results are illustrated on examples. AMS Subject Classification: 39A30, 39A60","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"20 1","pages":"187"},"PeriodicalIF":0.0,"publicationDate":"2020-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81345742","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":"THE SIZE MULTIPARTITE RAMSEY NUMBERS $m_j(P_n,K_{jtimes b})$","authors":"S. Sy, E. Effendi","doi":"10.12732/ijam.v33i2.9","DOIUrl":"https://doi.org/10.12732/ijam.v33i2.9","url":null,"abstract":"","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"38 1","pages":"305"},"PeriodicalIF":0.0,"publicationDate":"2020-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75700112","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}
Abstract: Graphon theory has recently begun attracting interdisciplinary research. Although the theory includes many intriguing concepts, one important aspect we often employ in network analysis is the relationship between the cut norm and operator norm of a graphon as an operator on some function spaces. This relationship is well known in the past arguments. However, the authors of the past works restricted the domain of a graphon to L∞(I). In this note, we discuss the relationship between the cut norm and operator norm of a graphon in more general situations. We improve the well-known existing inequality and enhance the accuracy of some lemma proofs.
{"title":"IMPROVING RESULTS FOR CUT AND OPERATOR NORMS ON GRAPHON","authors":"H. Honda","doi":"10.12732/ijam.v33i2.11","DOIUrl":"https://doi.org/10.12732/ijam.v33i2.11","url":null,"abstract":"Abstract: Graphon theory has recently begun attracting interdisciplinary research. Although the theory includes many intriguing concepts, one important aspect we often employ in network analysis is the relationship between the cut norm and operator norm of a graphon as an operator on some function spaces. This relationship is well known in the past arguments. However, the authors of the past works restricted the domain of a graphon to L∞(I). In this note, we discuss the relationship between the cut norm and operator norm of a graphon in more general situations. We improve the well-known existing inequality and enhance the accuracy of some lemma proofs.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"29 1","pages":"321"},"PeriodicalIF":0.0,"publicationDate":"2020-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89912520","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 report is devoted to one class so-called producing functionals and corresponding with its modeling generating spaces, some transformations building models equations and corresponding spaces are considered and investigated. It is shown that these transformations any point of Euclidean space Em-1 (generating spaces Mm-1) transfer into some corresponding points Em (or Mm) and conversely. It is also proposed one class general equations which are described many processes of chancing and generating spaces. Besides it is shown that processes of generating spaces are determined by some no depending prescribes points. Given others applications and from economics and physics.
{"title":"The Producing Functionals and its Applications","authors":"M. Yunusi","doi":"10.46300/91019.2020.7.1","DOIUrl":"https://doi.org/10.46300/91019.2020.7.1","url":null,"abstract":"The report is devoted to one class so-called producing functionals and corresponding with its modeling generating spaces, some transformations building models equations and corresponding spaces are considered and investigated. It is shown that these transformations any point of Euclidean space Em-1 (generating spaces Mm-1) transfer into some corresponding points Em (or Mm) and conversely. It is also proposed one class general equations which are described many processes of chancing and generating spaces. Besides it is shown that processes of generating spaces are determined by some no depending prescribes points. Given others applications and from economics and physics.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88883787","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}
Abstract: The present paper is devoted to the study of classical solution of an inverse boundary-value problem for the linearized equation of motion of a homogeneous elastic beam with an over-determination condition. The goal of the work is to determine both solution and the unknown coefficient together for the considered problem in the rectangular region. First, in order to investigate of solvability of the inverse problem, we reduce original problem to the auxiliary problem with trivial data. Applying the Fourier method and contraction mappings principle, the existence and uniqueness of the classical solution of the obtained equivalent problem is proved. Furthermore, using the equivalence, the unique solvability of the appropriate auxiliary inverse problem is shown.
{"title":"INVERSE BOUNDARY-VALUE PROBLEM FOR LINEARIZED EQUATION OF MOTION OF A HOMOGENEOUS ELASTIC BEAM","authors":"Kh.E. Abbasova, Y. Mehraliyev, E. Azizbayov","doi":"10.12732/IJAM.V33I1.12","DOIUrl":"https://doi.org/10.12732/IJAM.V33I1.12","url":null,"abstract":"Abstract: The present paper is devoted to the study of classical solution of an inverse boundary-value problem for the linearized equation of motion of a homogeneous elastic beam with an over-determination condition. The goal of the work is to determine both solution and the unknown coefficient together for the considered problem in the rectangular region. First, in order to investigate of solvability of the inverse problem, we reduce original problem to the auxiliary problem with trivial data. Applying the Fourier method and contraction mappings principle, the existence and uniqueness of the classical solution of the obtained equivalent problem is proved. Furthermore, using the equivalence, the unique solvability of the appropriate auxiliary inverse problem is shown.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"539 1","pages":"157"},"PeriodicalIF":0.0,"publicationDate":"2020-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77169324","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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