Unifying a multitude of common fixed point theorems in symmetric spaces

Abstract

The aim of this paper is to obtain some new common fixed point theorems for weakly compatible mappings in symmetric spaces satisfying an implicit function. Some illustrative examples to highlight the realized improvements are furnished. Our results generalize and extend some recent results contained in Ali and Imdad [Sarajevo J. Math. 4(17)(2008), 269-285] to symmetric spaces and consequently a host of metrical common fixed theorems are generalized and improved. We state an integral type fixed point theorem in symmetric space. In the process, we also derive a fixed point result on common fixed point in probabilistic symmetric spaces.

Fixed point theorems of generalized Gregus type in quasi-metric spaces for two pairs of mappings satisfying common coincidence range property

“…Other results in this topic are obtained in [12], [13], [14] and other papers. In [13] and [14], using implicit relations, the authors unified some common fixed point theorems for pairs of mappings satisfying common limit range property.…”

Fixed Point Theorems for Two Pairs of Mappings Satisfying a New Type of Common Limit Range Property in Gp Metric Spaces

“…Some fixed point results for pairs of mappings with CLR (S) and CLR (S,T ) --property are obtained in [15,17,18,23] and in other papers. Now we introduce a new type of common limit range property.…”

Fixed point theorems for two pairs of mappings satisfying a new type of common limit range property

“…Some fixed point results for pairs of mappings with CLR (S) and CLR (S,T) property are obtained in [19], [6], [20], [40] and in other papers.…”