The purpose of this paper is to show that a number of fixed point theorems are special cases of two theorems of Jungck and the author [6].
本文的目的是为了证明一些不动点定理是Jungck和作者[6]的两个定理的特例。
{"title":"Comments on some Fixed Point Theorems","authors":"B. Rhoades","doi":"10.30697/RFPTA-2018-001","DOIUrl":"https://doi.org/10.30697/RFPTA-2018-001","url":null,"abstract":"The purpose of this paper is to show that a number of fixed point theorems are special cases of two theorems of Jungck and the author [6].","PeriodicalId":119592,"journal":{"name":"Results in Fixed Point Theory and Applications","volume":"31 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130077525","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":"Approximating coupled coincidence points by alpha-dense curves","authors":"G. García","doi":"10.30697/RFPTA-2018-4","DOIUrl":"https://doi.org/10.30697/RFPTA-2018-4","url":null,"abstract":"","PeriodicalId":119592,"journal":{"name":"Results in Fixed Point Theory and Applications","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131500615","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 use C-class function in order to obtain some coupled fixed point theorems in the setting of Sb-metric space. Some results are also given in the form of corollaries. Examples are also given to verify our results.
{"title":"Fixed point theorems of $C$-class functions in $S_{b}$-metric space","authors":"D. Dhamodharan, Y. Rohen, A. H. Ansari","doi":"10.30697/rfpta-2018-018","DOIUrl":"https://doi.org/10.30697/rfpta-2018-018","url":null,"abstract":"In this paper, we use C-class function in order to obtain some coupled fixed point theorems in the setting of Sb-metric space. Some results are also given in the form of corollaries. Examples are also given to verify our results.","PeriodicalId":119592,"journal":{"name":"Results in Fixed Point Theory and Applications","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123669357","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 study some new fixed point results for self maps defined on partial metric type spaces. In particular, we give common fixed point theorems in the same setting. Some examples are given which illustrate the results.
{"title":"Fixed points on partial metric type spaces","authors":"Yaé Ulrich Gaba","doi":"10.30697/RFPTA-2019-009","DOIUrl":"https://doi.org/10.30697/RFPTA-2019-009","url":null,"abstract":"In this paper, we study some new fixed point results for self maps defined on partial metric type spaces. In particular, we give common fixed point theorems in the same setting. Some examples are given which illustrate the results.","PeriodicalId":119592,"journal":{"name":"Results in Fixed Point Theory and Applications","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127385416","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 propose two parallel extragradient-proximal methods for solving finite family of split equilibrium problems and split common fixed point problems, we call the problem split system of fixed point set constraint equilibrium problem (SSFPSCEP). The algorithms combine the extragradient method, the proximal method and the shrinking projection method. The weak and strong convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for equilibrium bifunctions. To obtain the strong convergence, we combine the first algorithm with the shrinking projection method in the second algorithm. Finally, appplication and one numerical experiment is given to demonstrate the efficiency of our algorithms.
{"title":"PARALLEL EXTRAGRADIENT-PROXIMAL METHODS FOR SOLVING SPLIT SYSTEM OF FIXED POINT SET CONSTRAINT EQUILIBRIUM PROBLEM IN REAL HILBERT SPACE","authors":"Anteneh Getachew Gebrie, R. Wangkeeree","doi":"10.30697/rfpta-2018-011","DOIUrl":"https://doi.org/10.30697/rfpta-2018-011","url":null,"abstract":"In this paper, we propose two parallel extragradient-proximal methods for solving finite family of split equilibrium problems and split common fixed point problems, we call the problem split system of fixed point set constraint equilibrium problem (SSFPSCEP). The algorithms combine the extragradient method, the proximal method and the shrinking projection method. The weak and strong convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for equilibrium bifunctions. To obtain the strong convergence, we combine the first algorithm with the shrinking projection method in the second algorithm. Finally, appplication and one numerical experiment is given to demonstrate the efficiency of our algorithms.","PeriodicalId":119592,"journal":{"name":"Results in Fixed Point Theory and Applications","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125768522","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":"On $alpha$-nonexpansive mapping and fixed-points in Banach spaces","authors":"P. Kaskasem, C. Klin-eam, S. Suantai","doi":"10.30697/RFPTA-2018-34","DOIUrl":"https://doi.org/10.30697/RFPTA-2018-34","url":null,"abstract":"","PeriodicalId":119592,"journal":{"name":"Results in Fixed Point Theory and Applications","volume":"278 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121031909","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}
Using control functions, we improve and extend some results of coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces by Lakshmikantam and Ćirić [5] to ordered M-metric spaces.
{"title":"Coupled fixed point theorems for generalized contractions in ordered $M$-metric spaces","authors":"Hossein Monfared, M. Asadi","doi":"10.30697/RFPTA-2018-004","DOIUrl":"https://doi.org/10.30697/RFPTA-2018-004","url":null,"abstract":"Using control functions, we improve and extend some results of coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces by Lakshmikantam and Ćirić [5] to ordered M-metric spaces.","PeriodicalId":119592,"journal":{"name":"Results in Fixed Point Theory and Applications","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123826734","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 study existence results for nonlocal initial value problems for fractional implicit differential equations with complex order. The Krasnoselkii’s fixed point theorem and Banach contraction principle are used for proving the main results. Moreover, we discuss the Ulam-Hyers stability.
{"title":"Existence and stability of fractional implicit differential equations with complex order","authors":"D. Vivek, K. Kanagarajan, E. Elsayed","doi":"10.30697/RFPTA-2018-27","DOIUrl":"https://doi.org/10.30697/RFPTA-2018-27","url":null,"abstract":"In this paper, we study existence results for nonlocal initial value problems for fractional implicit differential equations with complex order. The Krasnoselkii’s fixed point theorem and Banach contraction principle are used for proving the main results. Moreover, we discuss the Ulam-Hyers stability.","PeriodicalId":119592,"journal":{"name":"Results in Fixed Point Theory and Applications","volume":"271 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115834854","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 establish some common fixed point results for a pair of mappings in a metric space having the additional structure of a directed graph. The mappings are assumed to satisfy certain almost G-contractions without and with rational terms. Each of our results is illustrated with example. The approach here is a blending of analytic and graph theoretic methodologies.
{"title":"Common fixed point results in metric spaces endowed with a graph","authors":"B. Choudhury, N. Metiya, D. Khatua","doi":"10.30697/RFPTA-2018-18","DOIUrl":"https://doi.org/10.30697/RFPTA-2018-18","url":null,"abstract":"In this paper we establish some common fixed point results for a pair of mappings in a metric space having the additional structure of a directed graph. The mappings are assumed to satisfy certain almost G-contractions without and with rational terms. Each of our results is illustrated with example. The approach here is a blending of analytic and graph theoretic methodologies.","PeriodicalId":119592,"journal":{"name":"Results in Fixed Point Theory and Applications","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130787438","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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