Common fixed point theorems in connection with two weakly compatible mappings in menger space with bicomplex-valued metric

Abstract

. It is well-known that the fixed point theory plays a very important role in theory and applications. In 2017, Choi et al. [4] introduced the notion of bicomplex valued metric spaces (bi-CVMS) and established common fixed point results for weakly compatible mappings. On the other hand, in 1942, K. Menger [14] initiated the study of probabilistic metric spaces where he replaced the distance function d ( x,y ) by distribution function Fx,y ( t ), where the value of Fx,y ( t ) is interpreted as the probability that the distance between x and y be less than t , t > 0. In this paper, we have used bicomplex-valued metric on a set. We have taken Fx,y ( t ) as the probability that norm of the distance between x and y be less than t , i.e., || d ( x,y ) || < t , t > 0 and initiated menger space with bicomplex valued metric. We also aim to prove certain common fixed point theorems for a pair of weakly compatible mappings satisfying (CLRg) or (E.A) property in this space.