Uniqueness of Common Fixed Points for a Family of Mappings with <i>Φ</i>-Contractive Condition in 2-Metric Spaces

Abstract

In this paper, we will introduce a class of 5-dimensional functions  and prove that a family of self-mappings in 2-metric space have an unique common fixed point if 1)

New Unique Common Fixed Point Results for Four Mappings with Ф-Contractive Type in 2-Metric Spaces

“…But most of them held under subsidiary conditions [1][2][3], for examples: commutativity of mappings or uniform boundness of mappings at some point, and so on. In [4][5][6][7][8], the author obtained similar results for infinite mappings with generalized contractive or quasi-contractive conditions under removing the above subsidiary conditions. These results generalized and improved many same type unique common fixed point theorems.…”

A Family of Non-Self Maps Satisfying <i>Φ</i><sub>i</sub>-Contractive Condition and Having Unique Common Fixed Point in Metrically Convex Spaces

“…Those above results were discussed under some contractive conditions or certain boundary condition. Recently, the author discussed unique common fixed point theorems for a family of contractive or quasi-contractive type mappings on metrically convex spaces or 2-metric spaces, see [9][10][11][12][13], these results improve many known common fixed point theorems. In order to generalize and unify further these results, in this note, we shall discuss and obtain some unique common fixed point theorems for a family of more general non-self maps satisfying contractive condition on closed subset of a complete metrically convex metric space.…”