Four Mappings Satisfying Ψ-Contractive Type Condition and Having Unique Common Fixed Point on 2-Metric Spaces

Abstract

In this paper, we introduce a class Ψ of real functions defined on the set of non-negative real numbers, and obtain a new unique common fixed point theorem for four mappings satisfying Ψ-contractive condition on a non-complete 2-metric space and give the versions of the corresponding result for two and three mappings.

An Improvement of a Known Unique Common Fixed Point Result for Four Mappings on 2-Metric Spaces

“…The second author has obtained an unique common fixed point theorem for four mappings with  -contrac-tive condition [1,2] on 2-metric spaces in [1], where  is a continuous and non-decreasing real function on   0,  satisfying that for all . The re-sult generalizes and improves many corresponding results.…”

“…Here, we introduce a new class of real functions defined on    0,  , and reprove the well known unique common fixed point theorem for four mappings with  -contractive condition replaced by  -contractive condition on 2-metric spaces. The method used in this paper is very different from that in [1].…”