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Carpathian Journal of Mathematics最新文献

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An iterative method for variational inclusions and fixed points of total uniformly $L$-Lipschitzian mappings 全一致$L$-Lipschitzian映射的变分包含和不动点的迭代方法
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-30 DOI: 10.37193/cjm.2023.01.24
Q. Ansari, J. Balooee, S. Al-Homidan
{"title":"An iterative method for variational inclusions and fixed points of total uniformly $L$-Lipschitzian mappings","authors":"Q. Ansari, J. Balooee, S. Al-Homidan","doi":"10.37193/cjm.2023.01.24","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.24","url":null,"abstract":"\"The characterizations of $m$-relaxed monotone and maximal $m$-relaxed monotone operators are presented and by defining the resolvent operator associated with a maximal $m$-relaxed monotone operator, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. By using resolvent operator associated with a maximal $m$-relaxed monotone operator, an iterative algorithm is constructed for approximating a common element of the set of fixed points of a total uniformly $L$-Lipschitzian mapping and the set of solutions of a variational inclusion problem involving maximal $m$-relaxed monotone operators. By employing the concept of graph convergence for maximal $m$-relaxed monotone operators, a new equivalence relationship between the graph convergence of a sequence of maximal $m$-relaxed monotone operators and their associated resolvent operators, respectively, to a given maximal $m$-relaxed monotone operator and its associated resolvent operator is established. At the end, we study the strong convergence of the sequence generated by the proposed iterative algorithm to a common element of the above mentioned sets.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48641318","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}
引用次数: 0
Graphical Ekeland's variational principle with a generalized $w$-distance and a new approach to quasi-equilibrium problems 广义$w$-距离的图解Ekeland变分原理和拟平衡问题的新方法
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-30 DOI: 10.37193/cjm.2023.01.06
P. Chaipunya, Nantaporn Chuensupantharat, Printaporn Sanguansuttigul
{"title":"Graphical Ekeland's variational principle with a generalized $w$-distance and a new approach to quasi-equilibrium problems","authors":"P. Chaipunya, Nantaporn Chuensupantharat, Printaporn Sanguansuttigul","doi":"10.37193/cjm.2023.01.06","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.06","url":null,"abstract":"In this paper, we introduce the generalized Ekeland's variational principle in several forms. The general setting of our results includes a graphical metric structure and also employs a generalized $w$-distance. We then applied the proposed variational principles to obtain existence theorems for a class of quasi-equilibrium problems whose constraint maps are induced from the graphical structure. The conditions used in our existence results are based on a very general concept called a convergence class. Finally, we deduce the existence of a generalized Nash equilibrium via its quasi-equilibrium reformulation. A validating example is also presented.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49665277","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}
引用次数: 0
Some applications of idempotent elements in MV algebras 幂等元在MV代数中的一些应用
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-30 DOI: 10.37193/cjm.2023.01.10
C. Flaut
{"title":"Some applications of idempotent elements in MV algebras","authors":"C. Flaut","doi":"10.37193/cjm.2023.01.10","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.10","url":null,"abstract":"\"In this paper we provide some properties and applications of MV-algebras. We prove that a Fibonacci stationary sequence in an MV-algebra gives us an idempotent element. Moreover, taking into account of the representation of a finite MV-algebra, by using Boolean elements of this algebra, we prove that a Fibonacci sequence in an MV-algebra is always stationary. This result is interesting comparing with the behavior of such a sequence on the group $left( mathbb{Z}% _{n},+right) $, where the Fibonacci sequences are periodic, with the period given by the Pisano period. We also give some examples of finite MV-algebras and the number of their idempotent elements. As an application in Coding Theory, to a Boolean algebra it is attached a binary block code and it is proved that, under some conditions, the converse is also true.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70023834","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}
引用次数: 0
A novel approach for solving simultaneously one-parameter nonexpansive semigroup, convex minimization and fixed point problems involving set-valued operators 一种求解集值算子的单参数非扩张半群、凸极小和不动点问题的新方法
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-30 DOI: 10.37193/cjm.2023.01.23
T. Sow, A. Diene, N. Djitté
{"title":"A novel approach for solving simultaneously one-parameter nonexpansive semigroup, convex minimization and fixed point problems involving set-valued operators","authors":"T. Sow, A. Diene, N. Djitté","doi":"10.37193/cjm.2023.01.23","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.23","url":null,"abstract":"\"In this paper, we introduce a new iterative process for solving simultaneously one-parameter nonexpansive semigroup, convex minimization and fixed point problems involving set-valued operators in real Hilbert spaces and establish strong convergence theorems for the proposed iterative process. There is no compactness assumption. Our results improve important recent results.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41866773","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}
引用次数: 0
Most continuous and increasing functions have two different fixed points 大多数连续函数和递增函数都有两个不同的不动点
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-30 DOI: 10.37193/cjm.2023.01.15
S. Reich, A. Zaslavski
{"title":"Most continuous and increasing functions have two different fixed points","authors":"S. Reich, A. Zaslavski","doi":"10.37193/cjm.2023.01.15","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.15","url":null,"abstract":"\"We study the space of all continuous and increasing self-mappings of the real interval $[0,1]$ equipped with the topology of uniform convergence. In particular, we show that most such functions have at least two different fixed points.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48608167","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}
引用次数: 1
"Solutions of Split Equality Hammerstein Type Equation Problems in Reflexive Real Banach Spaces" “自反实Banach空间中分裂等式Hammerstein型方程问题的解”
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-30 DOI: 10.37193/cjm.2023.01.03
Y. Belay, H. Zegeye, O. A. Boikanyo
{"title":"\"Solutions of Split Equality Hammerstein Type Equation Problems in Reflexive Real Banach Spaces\"","authors":"Y. Belay, H. Zegeye, O. A. Boikanyo","doi":"10.37193/cjm.2023.01.03","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.03","url":null,"abstract":"\"The purpose of this study is to introduce an inertial algorithm for approximating a solution of the split equality Hammerstein type equation problem in general reflexive real Banach spaces. Strong convergence results are established under the assumption that the associated mappings are monotone and uniformly continuous. The results in this paper generalize and improve many of the existing results in the literature in the sense that the underlying mappings are relaxed from Lipschitz continuous to uniformly continuous and the spaces under consideration are extended from Hilbert spaces to reflexive real Banach spaces with a more general problem which includes the Hammerstein type equation problems.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43238444","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}
引用次数: 0
Relaxed modified Tseng algorithm for solving variational inclusion problems in real Banach spaces with applications 求解实Banach空间中变分包含问题的松弛修正Tseng算法及其应用
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-30 DOI: 10.37193/cjm.2023.01.01
A. Abubakar, Kumam Poom, Kitkuan Duangkamon, Padcharoen Anantachai
{"title":"Relaxed modified Tseng algorithm for solving variational inclusion problems in real Banach spaces with applications","authors":"A. Abubakar, Kumam Poom, Kitkuan Duangkamon, Padcharoen Anantachai","doi":"10.37193/cjm.2023.01.01","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.01","url":null,"abstract":"\"In this paper, relaxed and relaxed inertial modified Tseng algorithms for approximating zeros of sum of two monotone operators whose zeros are fixed points or J-fixed points of some nonexpansive-type mappings are introduced and studied. Strong convergence theorems are proved in the setting of real Banach spaces that are uniformly smooth and 2-uniformly convex. Furthermore, applications of the theorems to the concept of J-fixed point, convex minimization, image restoration and signal recovery problems are also presented. In addition, some interesting numerical implementations of our proposed methods in solving image recovery and compressed sensing problems are presented. Finally, the performance of our proposed methods are compared with that of some existing methods in the literature.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45075763","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}
引用次数: 4
Operators with Brownian unitary dilations 具有布朗酉扩张的算子
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-26 DOI: 10.37193/cjm.2022.03.08
Laurian Suciu
{"title":"Operators with Brownian unitary dilations","authors":"Laurian Suciu","doi":"10.37193/cjm.2022.03.08","DOIUrl":"https://doi.org/10.37193/cjm.2022.03.08","url":null,"abstract":"Certain bounded linear operators $T$ on a complex Hilbert space $h$ which have 2-isometric liftings $S$ on another space $ka supset h$ are being investigated. We refer also to a more special type of liftings, as well as to those which additionally meet the condition $S^*Sh subset h$. Furthermore we describe other types of dilations for $T$, which are close to 2-isometries. Among these we refer to expansive (concave) operators and also to Brownian unitary dilations. Different matrix representations for such operators are obtained, where matrix entries involve contractive operators.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49449420","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}
引用次数: 2
Some Fixed Point Results in Spaces with Perturbed Metrics 扰动度量空间中的一些不动点结果
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-26 DOI: 10.37193/cjm.2022.03.10
A. Branga, I. Olaru
{"title":"Some Fixed Point Results in Spaces with Perturbed Metrics","authors":"A. Branga, I. Olaru","doi":"10.37193/cjm.2022.03.10","DOIUrl":"https://doi.org/10.37193/cjm.2022.03.10","url":null,"abstract":"\"n this paper, the concept of perturbed metric was introduced within the metric spaces and some fixed point results were established for self-mappings satisfying such contractive conditions, using Picard operators technique and generalized contractions. Moreover, some applications of the main result to continuous data dependence of the fixed points of Picard operators defined on these spaces were presented. Also, the main result of this paper was applied to study the existence and uniqueness of the solution for an integral equation which models an epidemiological problem\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43258215","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}
引用次数: 1
"Lie symmetries of the nonlinear Fokker-Planck equation based on weighted Tsallis entropy" “基于加权Tsallis熵的非线性福克-普朗克方程的李对称性”
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-26 DOI: 10.37193/cjm.2022.03.07
C. Pripoae, I. Hiricǎ, G. Pripoae, V. Preda
{"title":"\"Lie symmetries of the nonlinear Fokker-Planck equation based on weighted Tsallis entropy\"","authors":"C. Pripoae, I. Hiricǎ, G. Pripoae, V. Preda","doi":"10.37193/cjm.2022.03.07","DOIUrl":"https://doi.org/10.37193/cjm.2022.03.07","url":null,"abstract":"\"We determine the nonlinear Fokker-Planck equation in one dimension, based on a weighted Tsallis entropy and we derive its associated Lie symmetries. The corresponding Lyapunov functions and Breg- man divergences are also found, together with a formula linking the drift function, the diffusion function and a diffusion constant. We solve the MaxEnt problem associated to the weighted Tsallis entropy.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44021908","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}
引用次数: 3
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