SOME COMMON FIXED POINTS THEOREMS FOR OCCASIONALLY WEAKLY COMPATIBLE MAPPINGS IN MENGER SPACE

Abstract

The fixed point theory as a part of the non-linear analysis is the study of function in metric or non-metric settings. K. Menger in1942 introduced the notion of probabilistic metric space (or statistical space or Menger Space) which is an important generalization of metric space and the study of this space was expanded rapidly with the pioneering work of B. Schweizer and A. Skalar [21] in 1960 and the work of V.M. Sehgal and A.T. Bharucha Reid [23] in 1972. This space broadens in weakly compatible in Menger space by Singh and Jain [24], B.D. Pant et. al [16] and this notion also extend to occasionally weakly compatible by AI. Thapagi and Shahzad [27]. The purpose of this paper is to establish a common fixed point result in Menger space in two pairs and three pairs of mappings by using occasionally weakly compatible mappings. Our first theorem generalizes the theorem of Sharma and Shahu [28] and B. Fisher et.al [29] and both theorems deduce some similar results in the literature.