Common fixed point theorems for generalized contraction mappings in modular metric spaces

Abstract

The notion of modular metric spaces being a natural generalization of classical modulars over linear spaces Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz, and Calderon-Lozanovskii spaces was recently introduced. Chistyakov [4, 6] introduced and studied the concept of modular metric spaces and proved fixed point theorems for contractive map in Modular spaces. It is related to contracting rather “generalized average velocities” than metric distances, and the successive approximations of fixed points converge to the fixed points in a weaker sense as compared to metric convergence. In this paper, we prove some unique common fixed point theorems for generalized contraction type mappings for six self occasionally weakly compatible mappings in modular metric spaces.