On the Existence of Solutions to a Boundary Value Problem via New Weakly Contractive Operator
In this paper, the notion of generalized quasi-weakly contractive operators in metric-like spaces is introduced, and new conditions for the existence of fixed points for such mappings are investigated. A non-trivial example which highlights the novelty of our principal idea is constructed. It is obs...
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| Published in: | Axioms Vol. 12; no. 4; p. 397 |
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| Main Authors: | , , , , , |
| Format: | Journal Article |
| Language: | English |
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01-04-2023
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| Abstract | In this paper, the notion of generalized quasi-weakly contractive operators in metric-like spaces is introduced, and new conditions for the existence of fixed points for such mappings are investigated. A non-trivial example which highlights the novelty of our principal idea is constructed. It is observed comparatively that the proposed concepts herein subsume some important results in the corresponding literature. As an application, one of our obtained findings is utilized to setup novel criteria for the existence of solutions to two-point boundary value problems of a second order differential equation. To attract new researchers in the directions examined in this article, a significant number of corollaries are pointed out and discussed. |
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| AbstractList | In this paper, the notion of generalized quasi-weakly contractive operators in metric-like spaces is introduced, and new conditions for the existence of fixed points for such mappings are investigated. A non-trivial example which highlights the novelty of our principal idea is constructed. It is observed comparatively that the proposed concepts herein subsume some important results in the corresponding literature. As an application, one of our obtained findings is utilized to setup novel criteria for the existence of solutions to two-point boundary value problems of a second order differential equation. To attract new researchers in the directions examined in this article, a significant number of corollaries are pointed out and discussed. |
| Audience | Academic |
| Author | Alotaibi, Trad Mohammed, OM Kalthum S. K. Shehu Shagari, Mohammed Chiroma, Rhoda Mustafa, Arafa O. Bakery, Awad A. |
| Author_xml | – sequence: 1 givenname: Rhoda surname: Chiroma fullname: Chiroma, Rhoda – sequence: 2 givenname: Trad orcidid: 0000-0001-9329-9483 surname: Alotaibi fullname: Alotaibi, Trad – sequence: 3 givenname: Mohammed surname: Shehu Shagari fullname: Shehu Shagari, Mohammed – sequence: 4 givenname: Awad A. orcidid: 0000-0001-6709-8012 surname: Bakery fullname: Bakery, Awad A. – sequence: 5 givenname: OM Kalthum S. K. surname: Mohammed fullname: Mohammed, OM Kalthum S. K. – sequence: 6 givenname: Arafa O. surname: Mustafa fullname: Mustafa, Arafa O. |
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| Cites_doi | 10.1186/1687-1812-2012-204 10.3934/math.2022986 10.1007/978-3-0348-8910-0_2 10.1186/s13663-018-0628-1 10.2307/2371174 10.1111/j.1749-6632.1994.tb44144.x 10.1016/j.mcm.2011.07.013 10.1007/s40590-021-00347-x 10.1016/j.jmaa.2005.03.087 |
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| References | Bakhtin (ref_1) 1989; 30 Chi (ref_11) 2013; 39 Mohammed (ref_14) 2021; 27 Jiddah (ref_15) 2022; 2022 Reich (ref_10) 2015; 16 Czerwik (ref_2) 1993; 1 Abdeljawad (ref_13) 2011; 54 (ref_12) 1974; 45 Mustafa (ref_4) 2006; 7 Matthews (ref_6) 1994; 728 (ref_7) 2012; 2012 Wilson (ref_5) 1931; 53 Jiddah (ref_16) 2022; 7 Cho (ref_9) 2012; 2018 Alber (ref_8) 1997; 98 Huang (ref_3) 2007; 332 |
| References_xml | – volume: 39 start-page: 369 year: 2013 ident: ref_11 article-title: On the fixed point theorems for generalized weakly contractive mappings on partial metric spaces publication-title: Bull. Iran. Math. Soc. contributor: fullname: Chi – volume: 1 start-page: 5 year: 1993 ident: ref_2 article-title: Contraction mappings in b-metric spaces publication-title: Acta Math. Inform. Univ. Ostrav. contributor: fullname: Czerwik – volume: 2012 start-page: 204 year: 2012 ident: ref_7 article-title: Metric-like spaces, partial metric spaces and fixed points publication-title: Fixed Point Theory Appl. doi: 10.1186/1687-1812-2012-204 – volume: 7 start-page: 17894 year: 2022 ident: ref_16 article-title: Fixed point results of a new family of hybrid contractions in generalized metric space with applications publication-title: AIMS Math. doi: 10.3934/math.2022986 contributor: fullname: Jiddah – volume: 98 start-page: 7 year: 1997 ident: ref_8 article-title: Principles of weakly contractive maps in Hilbert spaces publication-title: New Results in Operator Theory and Its Applications doi: 10.1007/978-3-0348-8910-0_2 contributor: fullname: Alber – volume: 2018 start-page: 3 year: 2012 ident: ref_9 article-title: Fixed point theorems for generalized weakly contractive mappings in metric spaces with application publication-title: Fixed Point Theory Appl. doi: 10.1186/s13663-018-0628-1 contributor: fullname: Cho – volume: 53 start-page: 675 year: 1931 ident: ref_5 article-title: On quasi-metric spaces publication-title: Am. J. Math. doi: 10.2307/2371174 contributor: fullname: Wilson – volume: 728 start-page: 183 year: 1994 ident: ref_6 article-title: Partial metric topology publication-title: Ann. N. Y. Acad. Sci. doi: 10.1111/j.1749-6632.1994.tb44144.x contributor: fullname: Matthews – volume: 54 start-page: 2923 year: 2011 ident: ref_13 article-title: Fixed points for generalized weakly contractive mappings in partial metric spaces publication-title: Math. Comput. Model. doi: 10.1016/j.mcm.2011.07.013 contributor: fullname: Abdeljawad – volume: 2022 start-page: 2205423 year: 2022 ident: ref_15 article-title: Fixed point results of Jaggi-type hybrid contraction in generalized metric space publication-title: J. Funct. Spaces contributor: fullname: Jiddah – volume: 7 start-page: 289 year: 2006 ident: ref_4 article-title: A new approach to generalized metric spaces publication-title: J. Nonlinear Convex Anal. contributor: fullname: Mustafa – volume: 16 start-page: 767 year: 2015 ident: ref_10 article-title: A remark on weakly contractive mappings publication-title: J. Nonlinear Covex Anal. contributor: fullname: Reich – volume: 27 start-page: 39 year: 2021 ident: ref_14 article-title: Fixed points of (φ, F)-weak contractions on metric-like spaces with applications to integral equations on time scales publication-title: Bol. Soc. Mat. Mex. doi: 10.1007/s40590-021-00347-x contributor: fullname: Mohammed – volume: 332 start-page: 1468 year: 2007 ident: ref_3 article-title: Cone metric spaces and fixed point theorems of contractive mappings publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2005.03.087 contributor: fullname: Huang – volume: 30 start-page: 26 year: 1989 ident: ref_1 article-title: The contraction mapping principle in quasi metric spaces publication-title: Funct. Anal. contributor: fullname: Bakhtin – volume: 45 start-page: 267 year: 1974 ident: ref_12 article-title: A generalization of Banach’s contraction principle publication-title: Proc. Am. Math. Soc. |
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| SubjectTerms | Boundary value problems Differential equations fixed point Investigations Mathematical research metric-like spaces Operator theory partial metric spaces weakly contractive |
| Title | On the Existence of Solutions to a Boundary Value Problem via New Weakly Contractive Operator |
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