A Relation-Theoretic Matkowski-Type Theorem in Symmetric Spaces
In this paper, we present a fixed-point theorem in R-complete regular symmetric spaces endowed with a locally T-transitive binary relation R using comparison functions that generalizes several relevant existing results. In addition, we adopt an example to substantiate the genuineness of our newly pr...
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| Vydáno v: | Axioms Ročník 10; číslo 2; s. 50 |
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| Abstract | In this paper, we present a fixed-point theorem in R-complete regular symmetric spaces endowed with a locally T-transitive binary relation R using comparison functions that generalizes several relevant existing results. In addition, we adopt an example to substantiate the genuineness of our newly proved result. Finally, as an application of our main result, we establish the existence and uniqueness of a solution of a periodic boundary value problem. |
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| AbstractList | In this paper, we present a fixed-point theorem in R-complete regular symmetric spaces endowed with a locally T-transitive binary relation R using comparison functions that generalizes several relevant existing results. In addition, we adopt an example to substantiate the genuineness of our newly proved result. Finally, as an application of our main result, we establish the existence and uniqueness of a solution of a periodic boundary value problem. |
| Author | Imdad, Mohammad Ali, Based Sessa, Salvatore |
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| Cites_doi | 10.1155/2008/562130 10.1186/1029-242X-2014-38 10.1007/s11083-005-9018-5 10.1016/S0362-546X(98)00002-9 10.2307/2370790 10.2478/dema-2014-0075 10.24193/fpt-ro.2018.1.02 10.4064/fm-3-1-133-181 10.1007/s11784-015-0233-4 10.1016/S1385-7258(68)50004-0 10.1016/j.jmaa.2005.07.004 10.1007/s11784-015-0247-y 10.1090/S0002-9939-1969-0239559-9 10.1515/JAA.1995.125 10.1007/s10114-005-0769-0 10.1090/S0002-9939-03-07220-4 |
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| Copyright | 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| References_xml | – volume: 2008 start-page: 562130 year: 2008 ident: ref_10 article-title: On coincidence and fixed-point theorems in symmetric spaces publication-title: Fixed Point Theory Appl. doi: 10.1155/2008/562130 – volume: 2014 start-page: 38 year: 2014 ident: ref_12 article-title: A new generalization of the Banach contraction principle publication-title: J. Inequalities Appl. doi: 10.1186/1029-242X-2014-38 – volume: 3 start-page: 156 year: 2003 ident: ref_7 article-title: Common fixed points under contractive conditions in symmetric spaces publication-title: Appl. Math. E-Notes – volume: 22 start-page: 223 year: 2005 ident: ref_17 article-title: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations publication-title: Order doi: 10.1007/s11083-005-9018-5 – volume: 36 start-page: 331 year: 1999 ident: ref_6 article-title: Fixed point theory in symmetric spaces with applications to probabilistic spaces publication-title: Nonlinear Anal. doi: 10.1016/S0362-546X(98)00002-9 – ident: ref_24 – volume: 53 start-page: 361 year: 1931 ident: ref_3 article-title: On semi-metric spaces publication-title: Am. J. Math. doi: 10.2307/2370790 – volume: 5 start-page: 171 year: 2005 ident: ref_8 article-title: Common fixed points for weakly compatible maps in symmetric spaces with application to probabilistic spaces publication-title: Appl. Math. E-Notes – volume: 47 start-page: 949 year: 2014 ident: ref_11 article-title: Hybrid fixed point theorems in semimetric spaces via common limit range property publication-title: Demonstr. Math. doi: 10.2478/dema-2014-0075 – volume: 19 start-page: 13 year: 2018 ident: ref_23 article-title: Nonlinear contractions in metric spaces under locally T-transitive binary relations publication-title: Fixed Point Theory doi: 10.24193/fpt-ro.2018.1.02 – volume: 3 start-page: 133 year: 1922 ident: ref_1 article-title: Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales publication-title: Fund. Math. doi: 10.4064/fm-3-1-133-181 – volume: 17 start-page: 541 year: 2015 ident: ref_4 article-title: Fixed points and Cauchy sequences in semimetric spaces publication-title: J. Fixed Point Theory Appl. doi: 10.1007/s11784-015-0233-4 – volume: 30 start-page: 27 year: 1968 ident: ref_13 article-title: On the convergence of successive approximations for nonlinear functional equations publication-title: Indag. Math. doi: 10.1016/S1385-7258(68)50004-0 – volume: 127 start-page: 5 year: 1975 ident: ref_20 article-title: Integrable solutions of functional equations publication-title: Diss. Math. Rozpr. Mat. – volume: 320 start-page: 352 year: 2006 ident: ref_9 article-title: Coincidence and fixed points in symmetric spaces under strict contractions publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2005.07.004 – volume: 11 start-page: 693 year: 2015 ident: ref_19 article-title: Relation-theoretic contraction principle publication-title: J. Fixed Point Theory Appl. doi: 10.1007/s11784-015-0247-y – volume: 19 start-page: 171 year: 1986 ident: ref_16 article-title: Fixed points for monotone iteratively local contractions publication-title: Demonstr. Math. – ident: ref_22 – volume: 20 start-page: 458 year: 1969 ident: ref_14 article-title: On nonlinear contractions publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-1969-0239559-9 – ident: ref_21 – volume: 1 start-page: 125 year: 1995 ident: ref_5 article-title: Nonlinear contractions on semimetric spaces publication-title: J. Appl. Anal. doi: 10.1515/JAA.1995.125 – volume: 23 start-page: 2205 year: 2007 ident: ref_18 article-title: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations publication-title: Acta Math. Sin. Engl. Ser. doi: 10.1007/s10114-005-0769-0 – volume: 5 start-page: 175 year: 1976 ident: ref_2 article-title: Questioni di completezza e contrazioni in spazi metrici generalizzati publication-title: Boll. Unione Mat. Ital. – volume: 132 start-page: 1435 year: 2004 ident: ref_15 article-title: A fixed point theorem in partially ordered sets and some applications to matrix equations publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-03-07220-4 |
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| SubjectTerms | binary relations Boundary value problems fixed points Fixed points (mathematics) Graphs regular spaces symmetric spaces T-transitivity Theorems |
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| Title | A Relation-Theoretic Matkowski-Type Theorem in Symmetric Spaces |
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