Pub Date : 2021-07-01DOI: 10.24193/fpt-ro.2021.2.60
R. Yan, Q. Ma, X. Ding
{"title":"Existence results for coupled nonlinear fractional differential equations with coupled strip and infinite point boundary conditions","authors":"R. Yan, Q. Ma, X. Ding","doi":"10.24193/fpt-ro.2021.2.60","DOIUrl":"https://doi.org/10.24193/fpt-ro.2021.2.60","url":null,"abstract":"","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42635240","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}
Pub Date : 2021-07-01DOI: 10.24193/fpt-ro.2021.2.42
R. Gopi, V. Pragadeeswarar
{"title":"Approximating common fixed point via Ishikawa's iteration","authors":"R. Gopi, V. Pragadeeswarar","doi":"10.24193/fpt-ro.2021.2.42","DOIUrl":"https://doi.org/10.24193/fpt-ro.2021.2.42","url":null,"abstract":"","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41821129","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}
Pub Date : 2021-07-01DOI: 10.24193/fpt-ro.2021.2.56
Y. Shehu
{"title":"Rate of convergence of modified Mann iteration for asymptotically nonexpansive mappings","authors":"Y. Shehu","doi":"10.24193/fpt-ro.2021.2.56","DOIUrl":"https://doi.org/10.24193/fpt-ro.2021.2.56","url":null,"abstract":"","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47665482","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}
Pub Date : 2021-07-01DOI: 10.24193/fpt-ro.2021.2.31
H. Akhadkulov, T. Y. Ying, A. Saaban, M. Noorani, H. Ibrahim
Fixed-point theory has experienced quick improvement over the most recent quite a few years. The development has been firmly advanced by the vast number of utilizations in the existence theory of functional, fractional, differential, partial differential, and integral equations. Two fundamental theorems concerning fixed points are those of Schauder and of Banach. The Schauder’s fixed point theorem, involving a compactness condition, may be stated as ”if S is a closed convex and bounded subset of a Banach space X, then every completely continuous operator A : S → S has at least one fixed point”. Note that an operator A on a Banach space X is called completely continuous if it is continuous and A(D) is totally bounded for any bounded subset D of X. Banach’s fixed point theorem, involving a metric assumption on the mapping, states that ”if X is complete metric space and if A is a contraction on X, then it has a unique fixed point, i.e., there is a unique point x∗ ∈ X such that Ax∗ = x∗. Moreover, the sequence Ax converges to x∗ for every x ∈ X,”. The idea of the hybrid fixed point theorems, that is, a blend of the nonlinear contraction principle and Schauder’s fixed-point theorem goes back to 1964, with Krasnoselskii [14], who still maintains an interest in the subject. He gave intriguing applications to differential equations by finding the existence of solutions under some hybrid conditions. Burton [4] extended Krasnoselskii’s result for a wide class of operators in 1998. In 2013, Dhage [6] and Dhage and Lakshmikantham [7] proposed an important Krasnoselskii-type fixed-point
{"title":"Notes on Krasnoselskii-type fixed-point theorems and their application to fractional hybrid differential problems","authors":"H. Akhadkulov, T. Y. Ying, A. Saaban, M. Noorani, H. Ibrahim","doi":"10.24193/fpt-ro.2021.2.31","DOIUrl":"https://doi.org/10.24193/fpt-ro.2021.2.31","url":null,"abstract":"Fixed-point theory has experienced quick improvement over the most recent quite a few years. The development has been firmly advanced by the vast number of utilizations in the existence theory of functional, fractional, differential, partial differential, and integral equations. Two fundamental theorems concerning fixed points are those of Schauder and of Banach. The Schauder’s fixed point theorem, involving a compactness condition, may be stated as ”if S is a closed convex and bounded subset of a Banach space X, then every completely continuous operator A : S → S has at least one fixed point”. Note that an operator A on a Banach space X is called completely continuous if it is continuous and A(D) is totally bounded for any bounded subset D of X. Banach’s fixed point theorem, involving a metric assumption on the mapping, states that ”if X is complete metric space and if A is a contraction on X, then it has a unique fixed point, i.e., there is a unique point x∗ ∈ X such that Ax∗ = x∗. Moreover, the sequence Ax converges to x∗ for every x ∈ X,”. The idea of the hybrid fixed point theorems, that is, a blend of the nonlinear contraction principle and Schauder’s fixed-point theorem goes back to 1964, with Krasnoselskii [14], who still maintains an interest in the subject. He gave intriguing applications to differential equations by finding the existence of solutions under some hybrid conditions. Burton [4] extended Krasnoselskii’s result for a wide class of operators in 1998. In 2013, Dhage [6] and Dhage and Lakshmikantham [7] proposed an important Krasnoselskii-type fixed-point","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43954656","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}
Pub Date : 2021-07-01DOI: 10.24193/fpt-ro.2021.2.34
A. Belhenniche, S. Benahmed, Francisco Câmara Pereira
{"title":"Extension of λ-PIR for weakly contractive operators via fixed point theory","authors":"A. Belhenniche, S. Benahmed, Francisco Câmara Pereira","doi":"10.24193/fpt-ro.2021.2.34","DOIUrl":"https://doi.org/10.24193/fpt-ro.2021.2.34","url":null,"abstract":"","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44869337","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}
Pub Date : 2021-07-01DOI: 10.24193/fpt-ro.2021.2.52
A. Petruşel, I. Rus, M. Serban
Let (X1,→) and (X2, ↪→) be two L-spaces, U be a nonempty subset of X1×X2 such that Ux1 := {x2 ∈ X2 | (x1, x2) ∈ U} is nonempty, for each x1 ∈ X1. Let T1 : X1 → X1, T2 : U → X2 be two operators and T : U → X1 ×X2 defined by T (x1, x2) := (T1(x1), T2(x1, x2)). If we suppose that T (U) ⊂ U , FT1 6= ∅ and FT2(x1,·) 6= ∅ for each x1 ∈ X1, the problem is in which additional conditions T is a weakly Picard operator ? In this paper we study this problem in the case when the convergence structures on X1 and X2 are defined by metrics. Some applications to the fixed point equations on spaces of continuous functions are also given.
{"title":"Some variants of fibre contraction principle and applications: from existence to the convergence of successive approximations","authors":"A. Petruşel, I. Rus, M. Serban","doi":"10.24193/fpt-ro.2021.2.52","DOIUrl":"https://doi.org/10.24193/fpt-ro.2021.2.52","url":null,"abstract":"Let (X1,→) and (X2, ↪→) be two L-spaces, U be a nonempty subset of X1×X2 such that Ux1 := {x2 ∈ X2 | (x1, x2) ∈ U} is nonempty, for each x1 ∈ X1. Let T1 : X1 → X1, T2 : U → X2 be two operators and T : U → X1 ×X2 defined by T (x1, x2) := (T1(x1), T2(x1, x2)). If we suppose that T (U) ⊂ U , FT1 6= ∅ and FT2(x1,·) 6= ∅ for each x1 ∈ X1, the problem is in which additional conditions T is a weakly Picard operator ? In this paper we study this problem in the case when the convergence structures on X1 and X2 are defined by metrics. Some applications to the fixed point equations on spaces of continuous functions are also given.","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":"35 37","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41331471","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}
Pub Date : 2021-07-01DOI: 10.24193/fpt-ro.2021.2.40
D. Dey, Raúl Fierro, M. Saha
{"title":"Fixed points and topological properties of extended quasi-metric spaces","authors":"D. Dey, Raúl Fierro, M. Saha","doi":"10.24193/fpt-ro.2021.2.40","DOIUrl":"https://doi.org/10.24193/fpt-ro.2021.2.40","url":null,"abstract":"","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49574765","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}
Pub Date : 2021-07-01DOI: 10.24193/fpt-ro.2021.2.44
H. Hashem, A. El-Sayed, R. Agarwal, B. Ahmad
. In this work, we are concerned with weak and pseudo solutions for some initial value problems of fractional order and their corresponding functional integral equation of fractional order. These initial value problems includes many initial value problems that arise in nonlinear analysis and its applications.
{"title":"Solvability of nonlinear functional differential equations of fractional order in reflexive Banach space","authors":"H. Hashem, A. El-Sayed, R. Agarwal, B. Ahmad","doi":"10.24193/fpt-ro.2021.2.44","DOIUrl":"https://doi.org/10.24193/fpt-ro.2021.2.44","url":null,"abstract":". In this work, we are concerned with weak and pseudo solutions for some initial value problems of fractional order and their corresponding functional integral equation of fractional order. These initial value problems includes many initial value problems that arise in nonlinear analysis and its applications.","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44816920","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}
Pub Date : 2021-07-01DOI: 10.24193/fpt-ro.2021.2.45
L. Jolaoso, M. Khamsi, O. Mewomo, C. C. Okeke
{"title":"On inertial type algorithms with generalized contraction mapping for solving monotone variational inclusion problems","authors":"L. Jolaoso, M. Khamsi, O. Mewomo, C. C. Okeke","doi":"10.24193/fpt-ro.2021.2.45","DOIUrl":"https://doi.org/10.24193/fpt-ro.2021.2.45","url":null,"abstract":"","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43875928","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}
Pub Date : 2021-07-01DOI: 10.24193/fpt-ro.2021.2.59
Oratai Yamaod, W. Sintunavarat
{"title":"Discussion of hybrid JS-contractions in b-metric spaces with applications to the existence of solutions for integral equations","authors":"Oratai Yamaod, W. Sintunavarat","doi":"10.24193/fpt-ro.2021.2.59","DOIUrl":"https://doi.org/10.24193/fpt-ro.2021.2.59","url":null,"abstract":"","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44271884","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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