Perturbed iterative approximation of common fixed points on nonlinear fuzzy and crisp mixed family operator equation couples in menger pn-spaces

Abstract

In this paper, based on the concept of probabilistic (ψ,ψ)- contractor couple introduced by Mihet, a new class of nonlinear operator equation couples with a mixed family of fuzzy and crisp operator equations in Menger probabilistic normed spaces (briefly, Menger PN-spaces) is introduced and studied. Further, some new iterative algorithms are constructed, and the existence of solutions for the nonlinear operator equation couples and the convergence of iterative sequences generated by the algorithms under a larger class of t-norms and joint orbitally complete conditions are discussed. © 2010 Springer-Verlag Berlin Heidelberg.