Common random fixed points of compatible random operators

Abstract

We construct a random iteration scheme and study necessary conditions for its convergence to a common random fixed point of two pairs of compatible random operators satisfying Meir-Keeler type conditions in Polish spaces. Some random fixed point theorems for weakly compatible random operators under generalized contractive conditions in the framework of symmetric spaces are also proved.

Random Common Fixed Point Theorem for Random Weakly Subsequentially Continuous Generalized Contractions With Application

“…A pair of self mappings F and T are weakly commuting if d(F T x, T F x) ≤ d(F x, T x), for all x ∈ X. In [14,15,20] the concepts of compatible, compatible of type (A), compatible of type (B), compatible of type (C), compatible of type (P ) and weakly compatible mappings are presented as a generalization of weakly commuting as follows: Two self mappings F and T are: (1) F T x n = T t , whenever {x n } is a sequence in X such that lim n→∞ F x n = lim n→∞ T x n = t, for some t ∈ X, (7) weakly compatible if F x = T x, x ∈ X implies F T x = T F x.…”

“…After paper of Bharucha-Ried [5], the field of random fixed point became most widely specially in functional analysis. A large number of researchers focussing on various aspects of random fixed point theory, some of these works see [3,1,12,[16][17][18].…”

Common Random Fixed Point theorem for compatible random multivalued operators

“…For multivalued mappings Itoh [9] obtained random analogues of corresponding deterministic result for different classes of mappings. Papageoriou [11], Beg [2,3], Beg and Shahzad [5] and Beg and Abbas [4] proved some common random fixed point and random coincidence point of a pair of compatible random operators.…”