On metrical fixed point theorems in symmetric spaces

Abstract

The aim of this paper is to obtain some common fixed point theorems for weakly compatible mappings in symmetric spaces satisfying generalized -contractive conditions under the common limit range property. Our results generalize and extend some recent results to symmetric spaces and consequently a host of metrical common fixed theorems are generalized and improved. In the process, we also derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any number of finite mappings. Some illustrative examples to highlight the realized improvements are also furnished.