Abstract
We prove the existence of a common random fixed point of two asymptotically nonexpansive random operators through strong and weak convergences of an iterative process. The necessary and sufficient condition for the convergence of sequence of measurable functions to a random fixed point of asymptotically quasi-nonexpansive random operators in uniformly convex Banach spaces is also established.
Highlights
Random nonlinear analysis is an important mathematical discipline which is mainly concerned with the study of random nonlinear operators and their properties and is needed for the study of various classes of random equations
Papageorgiou [25, 26], Beg [4, 5] studied common random fixed points and random coincidence points of a pair of compatible random operators and proved fixed point theorems for contractive random operators in Polish spaces
Let F be a nonempty closed, bounded, and convex subset of a separable uniformly convex Banach space X and let T, S : Ω × F → F be two continuous asymptotically nonexpansive random operators with sequence {kn} of real numbers in [1, ∞) satisfying
Summary
Random nonlinear analysis is an important mathematical discipline which is mainly concerned with the study of random nonlinear operators and their properties and is needed for the study of various classes of random equations. Itoh [18] extended Spacek’s and Hans’s theorem to multivalued contraction mappings. This theory has become the full fledged research area and various ideas associated with random fixed point theory are used to obtain the solution of nonlinear random system (see [6, 7, 9, 17, 29]). Papageorgiou [25, 26], Beg [4, 5] studied common random fixed points and random coincidence points of a pair of compatible random operators and proved fixed point theorems for contractive random operators in Polish spaces.
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