A System of Nonlinear Operator Equations for a Mixed Family of Fuzzy and Crisp Operators in Probabilistic Normed Spaces

Abstract

By using a random version of the theory of contractor introduced by Altman, we introduce and study a system of nonlinear operator equations for a mixed family of fuzzy and crisp operators in probabilistic normed spaces. We construct some new iterative algorithms for solving this kind of nonlinear operator equations. We also prove some new existence theorems of solutions of a new system of nonlinear operator equations for a mixed family of fuzzy and crisp operators and some new convergence results of sequences generated by iterative algorithms under joint orbitally complete conditions.

Coupled coincidence point theorems for contractions without commutative condition in intuitionistic fuzzy normed spaces

“…Several researchers have applied fuzzy theory to the well-known results in many fields, for example, quantum physics [20], nonlinear dynamical systems [21], population dynamics [22], computer programming [23], fixed point theorem [24][25][26][27], fuzzy stability problems [28][29][30], statistical convergence [31][32][33][34], functional equation [35], approximation theory [36], nonlinear equation [37,38] and many others.…”