Fixed points of multivalued contraction mappings in modular metric spaces

Afrah A.N. Abdou, Mohamed A. Khamsi

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19 Scopus citations

Abstract

The purpose of this paper is to study the existence of fixed points for contractive-type multivalued maps in the setting of modular metric spaces. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. In this paper we investigate the existence of fixed points of multivalued modular contractive mappings in modular metric spaces. Consequently, our results either generalize or improve fixed point results of Nadler (Pac. J. Math. 30:475-488, 1969) and Edelstein (Proc. Am. Math. Soc. 12:7-10, 1961). MSC: Primary 47H09; secondary 46B20; 47H10; 47E10.

Original languageBritish English
Article number249
JournalFixed Point Theory and Applications
Volume2014
Issue number1
DOIs
StatePublished - 2 Dec 2014

Keywords

  • fixed point
  • modular metric spaces
  • multivalued contraction mapping
  • Δ<inf>2</inf>-condition

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