Discrete mathematics, Complete quasimetric space, Applied Mathematics, Fixed point, Quasi-metric, Computational Mathematics, Metric space, Caristi fixed-point theorem, Mw-distance, Christian ministry, Caristi's fixed point theorem, MATEMATICA APLICADA, W-distance, Analysis, Mathematics
Abstract
[EN] In this paper we give a quasi-metric version of Caristi's fixed point theorem by using mw-distances. Our theorem generalizes a recent result obtained by Karapinar and Romaguera in [7], The authors thank the support of the Ministry of Economy and Competitiveness of Spain, Grants MTM2012-37894-C02-01 and MTM2015-64373-P (MINECO, FEDER,UE).
Pure mathematics, Property (philosophy), Mathematical analysis, Space (mathematics), Ekeland's variational principle, Metric space, Ekeland’s Variational Principle, Caristi’s fixed point theorem, If and only if, Variational principle, Geometry and Topology, Quasi-metric space, MATEMATICA APLICADA, Right K-sequentially complete, Mathematics
Abstract
[EN] We show that a quasi-metric space is right K-sequentially complete if and only if it satisfies the property of the weak form of Eke land's Variational Principle. This result solves a question raised by S. Cobzas (2011) [3]. (C) 2015 Elsevier B.V. All rights reserved., The authors are very grateful to the referee for a careful reading of the paper and several useful suggestions and comments which allowed a substantial improvement of the first version. Salvador Romaguera acknowledges the support of the Ministry of Economy and Competitiveness of Spain, Grant MTM2012-37894-C02-01
Published
2015
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