Stability and Strong Convergence Results for Random Jungck-Kirk-Noor Iterative Scheme

Abstract

Abstract. The purpose of this study is to introduce a JungckKirk-Noor type random iterative scheme and prove stability and strong convergence of this to establish a general theorem to approximate the unique common random coincidence point for two or more nonself random commuting mappings under general contractive condition in various spaces. Also we give the stability and convergence for random Jungck-Kirk-Ishikawa and random Jungck-Kirk-Mann as a corollaries. The results obtained in this paper improve the corresponding results announced recently.

Stability and convergence of new random approximation algorithms for random contractive-type operators in separable Hilbert spaces

“…, respectively while maintaining the convergence and stability results in [40]? Following the same argument as in [18] regarding the linear combination of the products of countably finite family of control parameters and the problems identified in each of the iterative schemes studied, the aim of this paper is to provide an affirmative answer to Question 1.1.…”

“…Definition 2.2. (see, e.g., [40]) For two random operators S, Γ : Ω × D −→ E with Γ(ξ, D) ⊆ S(ξ, D) and C is a nonempty closed and convex subset of a separable Banach space E, there exist real numbers η ∈ [0, 1], δ ∈ [0, 1) and a monotone increasing function φ : R + −→ R + with φ(0) = 0 and ∀x, y ∈ C, we get…”

“…Let (Ω, Σ) be a measurable space (Ω − a set and Σ − sigma algebra), D a nonempty closed and convex subset of a real separable Banach space E and Γ : Ω −→ D a given mapping. Then, To approximate the fixed point of random mappings, different fixed point iterative schemes have been used by different authors (see, for example, [14], [40], [42], [43] and the reference therein).…”

“…Recently, Rashwan and Hammad [40] introduced the following random version of Jungck-Kirk-Noor iterative scheme defined in [24]: Let Γ, S : Ω × Z −→ Y be two random mappings defined on a nonempty closed and convex subset D of a separable Banach space Y . Let x 0 : Ω −→ D be an arbitrary measurable mapping.…”

On the Equivalence of Stochastic Fixed Point Iterations for Generalized φ-Contractive-Like Operators

“…Random fixed point theorems for random contraction mappings on separable complete metric spaces were first proved by Spacek [1] and Hans (see [2,3]). Random fixed point theory has become the full-fledged research area and various ideas associated with the theory are applied to obtain the solutions to a class of stochastic integral equations (see [4,5]). Random fixed theorems are well known stochastic generalizations of classical fixed point theorems and are usually needed in the theory of random equations, random matrices, random differential equations, and different classes of random operators emanating in physical systems [6,7].…”