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.