On extended versions of Dancs-Hegedüs-Medvegyev's fixed-point theorem. (3rd June 2017)

• Record Type: Journal Article
• Authors: Bao, Truong Q.; Théra, Michel A.
• Is Part Of: Optimization. Volume 66:Number 6(2017)
• Page Start: 875
• Page End: 887
• Publication Date: 2017-06-03
• Subjects: Ekeland variational principle -- fixed point -- Quasi metric -- forward Cauchy sequence -- forward convergence; 49J53 -- 49J52 -- 47J30 -- 54H25 -- 90C29 -- 90C30; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2015.1113533
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this article, we establish some fixed-point (known also as critical point, invariant point) theorems in quasi-metric spaces . Our results unify and further extend in some regards the fixed-point theorem proposed by Dancs, S.; Hegedüs, M.; Medvegyev, P. (A general ordering and fixed-point principle in complete metric space. Acta Sci. Math. 1983;46:381–388), the results given by Khanh, P.Q., Quy D.N. (A generalized distance and enhanced Ekeland?s variational principle for vector functions. Nonlinear Anal. 2010;73:2245–2259), the preorder principles established by Qiu, J.H. (A pre-order principle and set-valued Ekeland variational principle. J. Math. Anal. Appl. 2014;419:904–937) and the results obtained by Bao, T.Q., Mordukhovich, B.S., Soubeyran, A. (Fixed points and variational principles with applications to capability theory of wellbeing via variational rationality. Set-Valued Var. Anal. 2015;23:375–398). In addition, we provide examples to illustrate that the improvements of our results are significant.