Pub Date : 2022-01-02DOI: 10.24193/fpt-ro.2022.1.15
J. Ferrer, E. Llorens-Fuster
{"title":"A fixed point dichotomy","authors":"J. Ferrer, E. Llorens-Fuster","doi":"10.24193/fpt-ro.2022.1.15","DOIUrl":"https://doi.org/10.24193/fpt-ro.2022.1.15","url":null,"abstract":"","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46270978","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 : 2022-01-02DOI: 10.24193/fpt-ro.2022.1.01
H. Abass, A. A. Mebawondu, C. Izuchukwu, O. K. Narain
{"title":"On split common fixed point and monotone inclusion problems in reflexive Banach spaces","authors":"H. Abass, A. A. Mebawondu, C. Izuchukwu, O. K. Narain","doi":"10.24193/fpt-ro.2022.1.01","DOIUrl":"https://doi.org/10.24193/fpt-ro.2022.1.01","url":null,"abstract":"","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46323017","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 : 2022-01-02DOI: 10.24193/fpt-ro.2022.1.13
V. Colao
{"title":"A note on the rate of convergence of viscosity iterations","authors":"V. Colao","doi":"10.24193/fpt-ro.2022.1.13","DOIUrl":"https://doi.org/10.24193/fpt-ro.2022.1.13","url":null,"abstract":"","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42551843","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 : 2022-01-02DOI: 10.24193/fpt-ro.2022.1.25
Bing Tan, A. Petruşel, X. Qin, J. Yao
. In this paper, we investigate three new relaxed single projection methods with alternating inertial extrapolation steps and adaptive non-monotonic step sizes for solving pseudo-monotone variational inequalities in real Hilbert spaces. The proposed algorithms need to compute the projection on the feasible set only once in each iteration and they can work adaptively without the prior information of the Lipschitz constant of the mapping. The weak convergence theorems of the proposed iterative schemes are established under some appropriate conditions imposed on the parameters. These methods recover the Fej´er monotonicity of the even subsequence with respect to the solution and obtain linear convergence rates. Finally, some numerical experiments and applications to optimal control problems are provided to demonstrate the advantages and efficiency of the proposed methods compared to some recent related ones.
{"title":"Global and linear convergence of alternated inertial single projection algorithms for pseudo-monotone variational inequalities","authors":"Bing Tan, A. Petruşel, X. Qin, J. Yao","doi":"10.24193/fpt-ro.2022.1.25","DOIUrl":"https://doi.org/10.24193/fpt-ro.2022.1.25","url":null,"abstract":". In this paper, we investigate three new relaxed single projection methods with alternating inertial extrapolation steps and adaptive non-monotonic step sizes for solving pseudo-monotone variational inequalities in real Hilbert spaces. The proposed algorithms need to compute the projection on the feasible set only once in each iteration and they can work adaptively without the prior information of the Lipschitz constant of the mapping. The weak convergence theorems of the proposed iterative schemes are established under some appropriate conditions imposed on the parameters. These methods recover the Fej´er monotonicity of the even subsequence with respect to the solution and obtain linear convergence rates. Finally, some numerical experiments and applications to optimal control problems are provided to demonstrate the advantages and efficiency of the proposed methods compared to some recent related ones.","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49241675","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 : 2022-01-02DOI: 10.24193/fpt-ro.2022.1.12
B. Choi
{"title":"Δ-convergence of convex combinations of two maps on p-uniformly convex metric spaces","authors":"B. Choi","doi":"10.24193/fpt-ro.2022.1.12","DOIUrl":"https://doi.org/10.24193/fpt-ro.2022.1.12","url":null,"abstract":"","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46110931","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 : 2022-01-02DOI: 10.24193/fpt-ro.2022.1.02
S. Abbas, M. Benchohra, A. Petruşel
{"title":"Coupled Hilfer and Hadamard fractional differential systems in generalized Banach spaces","authors":"S. Abbas, M. Benchohra, A. Petruşel","doi":"10.24193/fpt-ro.2022.1.02","DOIUrl":"https://doi.org/10.24193/fpt-ro.2022.1.02","url":null,"abstract":"","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42010978","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 : 2022-01-02DOI: 10.24193/fpt-ro.2022.1.19
Do Lan, Vu Nam Phong
{"title":"Decay solutions to retarded fractional evolution inclusions with superlinear perturbations","authors":"Do Lan, Vu Nam Phong","doi":"10.24193/fpt-ro.2022.1.19","DOIUrl":"https://doi.org/10.24193/fpt-ro.2022.1.19","url":null,"abstract":"","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45119153","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 : 2022-01-02DOI: 10.24193/fpt-ro.2022.1.20
E. A. P. Quiroz, S. C. Acuña
{"title":"Linear and superlinear convergence of an inexact algorithm with proximal distances for variational inequality problems","authors":"E. A. P. Quiroz, S. C. Acuña","doi":"10.24193/fpt-ro.2022.1.20","DOIUrl":"https://doi.org/10.24193/fpt-ro.2022.1.20","url":null,"abstract":"","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48780683","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 : 2022-01-02DOI: 10.24193/fpt-ro.2022.1.05
M. Alfuraidan, M. Khamsi, K. Saleh
{"title":"On asymptotically nonexpansive mappings with non-convex domains","authors":"M. Alfuraidan, M. Khamsi, K. Saleh","doi":"10.24193/fpt-ro.2022.1.05","DOIUrl":"https://doi.org/10.24193/fpt-ro.2022.1.05","url":null,"abstract":"","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45336343","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 : 2022-01-02DOI: 10.24193/fpt-ro.2022.1.08
M. Asaduzzaman, Md. Zulfikar Ali
. In this article, the existence criteria of at least one or at least three positive solutions to the Caputo-type nonlinear fractional differential equation with integral boundary value conditions has been established. The method applied in this study is formulated by the well-known Guo-Krasnoselskii’s fixed point theorem and Leggett-Williams fixed point theorem. First, the Green’s function for corresponding linear fractional differential equation of the main nonlinear fractional differential equation under same boundary value conditions has been constructed. Next, several essential properties of that Green’s function have been proved. Finally, in cone spaces some new existence and multiplicity results for the Caputo-type nonlinear fractional differential equation with integral boundary value conditions are obtained. To support the analytic proof appropriate illustrative examples has also been discussed.
{"title":"Existence of multiple positive solutions to the Caputo-type nonlinear fractional differential equation with integral boundary value conditions","authors":"M. Asaduzzaman, Md. Zulfikar Ali","doi":"10.24193/fpt-ro.2022.1.08","DOIUrl":"https://doi.org/10.24193/fpt-ro.2022.1.08","url":null,"abstract":". In this article, the existence criteria of at least one or at least three positive solutions to the Caputo-type nonlinear fractional differential equation with integral boundary value conditions has been established. The method applied in this study is formulated by the well-known Guo-Krasnoselskii’s fixed point theorem and Leggett-Williams fixed point theorem. First, the Green’s function for corresponding linear fractional differential equation of the main nonlinear fractional differential equation under same boundary value conditions has been constructed. Next, several essential properties of that Green’s function have been proved. Finally, in cone spaces some new existence and multiplicity results for the Caputo-type nonlinear fractional differential equation with integral boundary value conditions are obtained. To support the analytic proof appropriate illustrative examples has also been discussed.","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47672124","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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