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":" ","pages":""},"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}
Pub Date : 2022-01-02DOI: 10.24193/fpt-ro.2022.1.03
Abderrahim El Adraoui, M. Kabil, S. Lazaiz
{"title":"Generalized metric spaces and some related fixed point theorems","authors":"Abderrahim El Adraoui, M. Kabil, S. Lazaiz","doi":"10.24193/fpt-ro.2022.1.03","DOIUrl":"https://doi.org/10.24193/fpt-ro.2022.1.03","url":null,"abstract":"","PeriodicalId":51051,"journal":{"name":"Fixed Point Theory","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42222194","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.2021.2.37
Lili Chen, N. Yang, Yanfeng Zhao
{"title":"Mann iterative algorithm in convex metric spaces endowed with a directed graph","authors":"Lili Chen, N. Yang, Yanfeng Zhao","doi":"10.24193/fpt-ro.2021.2.37","DOIUrl":"https://doi.org/10.24193/fpt-ro.2021.2.37","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":"47953697","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.2021.2.47
M. Khoshhal, D. E. Bagha
{"title":"Existence and approximation of fixed points of λ-hybrid mappings in complete CAT(0) spaces","authors":"M. Khoshhal, D. E. Bagha","doi":"10.24193/fpt-ro.2021.2.47","DOIUrl":"https://doi.org/10.24193/fpt-ro.2021.2.47","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":"44993614","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.2021.2.61
Liu Yang, Hui Zhou, Chunfang Shen
Authors’ abstract: In this paper, by using the Guo-Krasnoselskii theorem, we investigate the existence and nonexistence of positive solutions of a class of boundary value problem of third-order nonlinear differential equation involving Stieltjes integral conditions. Under some growth conditions imposed on the nonlinear term, we obtain explicit ranges of values of parameters with which the problem has a positive solution and has no positive solution respectively. An example is given to illustrate the main results of the paper.
{"title":"Positive solutions of nonlinear third-order boundary value problems involving Stieltjes integral conditions","authors":"Liu Yang, Hui Zhou, Chunfang Shen","doi":"10.24193/fpt-ro.2021.2.61","DOIUrl":"https://doi.org/10.24193/fpt-ro.2021.2.61","url":null,"abstract":"Authors’ abstract: In this paper, by using the Guo-Krasnoselskii theorem, we investigate the existence and nonexistence of positive solutions of a class of boundary value problem of third-order nonlinear differential equation involving Stieltjes integral conditions. Under some growth conditions imposed on the nonlinear term, we obtain explicit ranges of values of parameters with which the problem has a positive solution and has no positive solution respectively. An example is given to illustrate the main results of the paper.","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":"46063069","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.2021.2.48
D. Loi, V. Luong, N. T. Tung
In this paper, nonlinear differential evolution equations of fractional order in Banach spaces involving unbounded delays are investigated. We aim to prove the existence of mild solutions and demonstrate its polynomial decay by the fixed point principle for condensing maps. An example of the application of abstract results is given for illustration.
{"title":"Decay estimates for two-term time fractional differential equations with infinite delays","authors":"D. Loi, V. Luong, N. T. Tung","doi":"10.24193/fpt-ro.2021.2.48","DOIUrl":"https://doi.org/10.24193/fpt-ro.2021.2.48","url":null,"abstract":"In this paper, nonlinear differential evolution equations of fractional order in Banach spaces involving unbounded delays are investigated. We aim to prove the existence of mild solutions and demonstrate its polynomial decay by the fixed point principle for condensing maps. An example of the application of abstract results is given for illustration.","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":"47912146","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.2021.2.57
S. Shukri
{"title":"Geometrical properties of lp spaces","authors":"S. Shukri","doi":"10.24193/fpt-ro.2021.2.57","DOIUrl":"https://doi.org/10.24193/fpt-ro.2021.2.57","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":"48513377","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.2021.2.32
A. Amar, Hajer Garbout, D. O’Regan
{"title":"Surjectivity results for nonlinear weakly sequentially continuous operators and applications","authors":"A. Amar, Hajer Garbout, D. O’Regan","doi":"10.24193/fpt-ro.2021.2.32","DOIUrl":"https://doi.org/10.24193/fpt-ro.2021.2.32","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":"46900374","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.2021.2.50
D. O’Regan
In this paper we present a variety of Leray–Schauder type continuation theorems for general classes of weakly Mönch type maps.
本文给出了一般弱Mönch型映射类的Leray-Schauder型延拓定理。
{"title":"Essential weakly Mönch type maps and continuation theory","authors":"D. O’Regan","doi":"10.24193/fpt-ro.2021.2.50","DOIUrl":"https://doi.org/10.24193/fpt-ro.2021.2.50","url":null,"abstract":"In this paper we present a variety of Leray–Schauder type continuation theorems for general classes of weakly Mönch type maps.","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":"46198765","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.2021.2.46
S. Karmakar, Hiranmoy Garai, L. Dey, A. Chanda
. In this article, we introduce the notions of F -contractions and Hardy-Rogers type F - contractions via w -distances in the backdrop of an orthogonal metric space. After this, we prove some fixed point results concerning the said kind of contractions by taking a weaker version of completeness of the underlying space instead of completeness. Further, we employ the results to obtain some existence and uniqueness criteria of the solution(s) to a certain type of second order initial value and boundary value problems. Along with these, we illustrate some numerical examples to interpret our achieved fixed point results.
{"title":"Solution to second order differential equations via Fw-contractions","authors":"S. Karmakar, Hiranmoy Garai, L. Dey, A. Chanda","doi":"10.24193/fpt-ro.2021.2.46","DOIUrl":"https://doi.org/10.24193/fpt-ro.2021.2.46","url":null,"abstract":". In this article, we introduce the notions of F -contractions and Hardy-Rogers type F - contractions via w -distances in the backdrop of an orthogonal metric space. After this, we prove some fixed point results concerning the said kind of contractions by taking a weaker version of completeness of the underlying space instead of completeness. Further, we employ the results to obtain some existence and uniqueness criteria of the solution(s) to a certain type of second order initial value and boundary value problems. Along with these, we illustrate some numerical examples to interpret our achieved fixed point results.","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":"42596181","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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