Common fixed point theorems in Menger probabilistic metric spaces using the CLRg property

Abstract

Under some weaker conditions of the ϕ, some common fixed point theorems for weakly compatible mappings are established in Menger probabilistic metric spaces. Using the CLRg property, our results show that the completeness of underlying spaces is not necessary for fixed point theorems. In order to illustrate our results, we provide two examples in which other theorems cannot be applied.

Best approximation of κ-random operator inequalities in matrix MB-algebras

“…In this paper, we study distribution functions with the ranges in a class of matrix algebras [1][2][3] and introduce the concept of a matrix Menger normed algebra using the generalized triangular norm which is a generalization of an MB-algebra [4], i.e., a Menger normed space with algebraic structures [5][6][7][8]. This concept helps us to study intuitionistic spaces and their generalization, i.e., neutrosophic spaces introduced by Smarandache [9,10].…”