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Generalized Contraction and Invariant Approximation Resultson Nonconvex Subsets of Normed Spaces

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Generalized Contraction and Invariant Approximation Resultson Nonconvex Subsets of Normed Spaces

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dc.contributor.author Abbas, Mujahid es_ES
dc.contributor.author Ali, Basit es_ES
dc.contributor.author Romaguera Bonilla, Salvador es_ES
dc.date.accessioned 2014-09-26T12:55:39Z
dc.date.available 2014-09-26T12:55:39Z
dc.date.issued 2014
dc.identifier.issn 1085-3375
dc.identifier.uri http://hdl.handle.net/10251/40319
dc.description.abstract Wardowski (2012) introduced a new type of contractive mapping and proved a fixed point result in complete metric spaces as a generalization of Banach contraction principle. In this paper, we introduce a notion of generalized F-contraction mappings which is used to prove a fixed point result for generalized nonexpansive mappings on star-shaped subsets of normed linear spaces. Some theorems on invariant approximations in normed linear spaces are also deduced. Our results extend, unify, and generalize comparable results in the literature. es_ES
dc.description.sponsorship The authors are very grateful to the referees for their valuable comments and suggestions, and, in particular, to one of them for calling our attention on the crucial fact stated in the first part of Remark 5 and for the elegant reformulation of Theorem 13 stated in Remark 14. Salvador Romaguera acknowledges the support of the Universitat Politecnica de Valencia, Grant PAID-06-12-SP20120471. en_EN
dc.language Inglés es_ES
dc.publisher Hindawi Publishing Corporation es_ES
dc.relation.ispartof Abstract and Applied Analysis es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Fixed points theorems es_ES
dc.subject Banach spaces es_ES
dc.subject Metric spaces es_ES
dc.subject Mappings es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Generalized Contraction and Invariant Approximation Resultson Nonconvex Subsets of Normed Spaces es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1155/2014/391952
dc.relation.projectID info:eu-repo/grantAgreement/UPV//PAID-06-12-SP20120471/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.contributor.affiliation Universitat Politècnica de València. Instituto Universitario de Matemática Pura y Aplicada - Institut Universitari de Matemàtica Pura i Aplicada es_ES
dc.description.bibliographicCitation Abbas, M.; Ali, B.; Romaguera Bonilla, S. (2014). Generalized Contraction and Invariant Approximation Resultson Nonconvex Subsets of Normed Spaces. Abstract and Applied Analysis. 2014:1-5. https://doi.org/10.1155/2014/391952 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1155/2014/391952 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 5 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 2014 es_ES
dc.relation.senia 265734
dc.contributor.funder Universitat Politècnica de València es_ES
dc.description.references Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta Mathematicae, 3, 133-181. doi:10.4064/fm-3-1-133-181 es_ES
dc.description.references Arandjelović, I., Kadelburg, Z., & Radenović, S. (2011). Boyd–Wong-type common fixed point results in cone metric spaces. Applied Mathematics and Computation, 217(17), 7167-7171. doi:10.1016/j.amc.2011.01.113 es_ES
dc.description.references Boyd, D. W., & Wong, J. S. W. (1969). On nonlinear contractions. Proceedings of the American Mathematical Society, 20(2), 458-458. doi:10.1090/s0002-9939-1969-0239559-9 es_ES
dc.description.references Huang, L.-G., & Zhang, X. (2007). Cone metric spaces and fixed point theorems of contractive mappings. Journal of Mathematical Analysis and Applications, 332(2), 1468-1476. doi:10.1016/j.jmaa.2005.03.087 es_ES
dc.description.references Rakotch, E. (1962). A note on contractive mappings. Proceedings of the American Mathematical Society, 13(3), 459-459. doi:10.1090/s0002-9939-1962-0148046-1 es_ES
dc.description.references Tarafdar, E. (1974). An approach to fixed-point theorems on uniform spaces. Transactions of the American Mathematical Society, 191, 209-209. doi:10.1090/s0002-9947-1974-0362283-5 es_ES
dc.description.references Dix, J. G., & Karakostas, G. L. (2009). A fixed-point theorem for S-type operators on Banach spaces and its applications to boundary-value problems. Nonlinear Analysis: Theory, Methods & Applications, 71(9), 3872-3880. doi:10.1016/j.na.2009.02.057 es_ES
dc.description.references Latrach, K., Aziz Taoudi, M., & Zeghal, A. (2006). Some fixed point theorems of the Schauder and the Krasnosel’skii type and application to nonlinear transport equations. Journal of Differential Equations, 221(1), 256-271. doi:10.1016/j.jde.2005.04.010 es_ES
dc.description.references Meinardus, G. (1963). Invarianz bei linearen Approximationen. Archive for Rational Mechanics and Analysis, 14(1), 301-303. doi:10.1007/bf00250708 es_ES
dc.description.references Habiniak, L. (1989). Fixed point theorems and invariant approximations. Journal of Approximation Theory, 56(3), 241-244. doi:10.1016/0021-9045(89)90113-5 es_ES
dc.description.references Hicks, T. ., & Humphries, M. . (1982). A note on fixed-point theorems. Journal of Approximation Theory, 34(3), 221-225. doi:10.1016/0021-9045(82)90012-0 es_ES
dc.description.references Singh, S. . (1979). An application of a fixed-point theorem to approximation theory. Journal of Approximation Theory, 25(1), 89-90. doi:10.1016/0021-9045(79)90036-4 es_ES
dc.description.references Subrahmanyam, P. . (1977). An application of a fixed point theorem to best approximation. Journal of Approximation Theory, 20(2), 165-172. doi:10.1016/0021-9045(77)90070-3 es_ES
dc.description.references Wardowski, D. (2012). Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory and Applications, 2012(1). doi:10.1186/1687-1812-2012-94 es_ES
dc.description.references Abbas, M., Ali, B., & Romaguera, S. (2013). Fixed and periodic points of generalized contractions in metric spaces. Fixed Point Theory and Applications, 2013(1), 243. doi:10.1186/1687-1812-2013-243 es_ES


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