Fixed Points of Various Types of Operators in Modular Metric Spaces

Sumana Pal, Ansar Gazi

Abstract

This paper is mainly devoted to the study of fixed point theorems for generalized contractive type mappings over a complete modular metric space. A new approach for obtaining fixed point result using a Cantor's Intersection like Theorem on modular metric spaces has been investigated. The notion of orbital completeness has been exploited in search of fixed point for Caristi-type mapping. We also explore a result on fixed points for \'Ciri\'c operator over a complete modular metric space. Further we give a result on common fixed point which extends a result due to Jungck.