Let K be a subset of a real normed linear space E and let T be a self-mapping on K . T is said to be nonexpansive provided ‖Tx−Ty‖ ‖x− y‖ for all x, y ∈ K . Fixed-point iteration process for nonexpansive mappings in Banach spaces including Mann and Ishikawa iteration processes has been studied extensively by many authors to solve the nonlinear operator equations in Hilbert spaces and Banach spa...

A mixed monotone variational inequality MMVI problem in a Hilbert space H is formulated to find a point u∗ ∈ H such that 〈Tu∗, v − u∗〉 φ v − φ u∗ ≥ 0 for all v ∈ H, where T is a monotone operator and φ is a proper, convex, and lower semicontinuous function onH. Iterative algorithms are usually applied to find a solution of an MMVI problem. We show that the iterative algorithm introduced in the ...

in this paper by using the idea of mean convergence, weintroduce an iterative scheme for finding a common element of theset of solutions of an equilibrium problem and the fixed points setof a nonspreading-type mappings in hilbert space. a strongconvergence theorem of the proposed iterative scheme is establishedunder some control conditions. the main result of this paper extendthe results obtain...

Abstract In this paper, we study and analyze an iterative method for solving nonlinear equations with ninth order of convergence. The new proposed method is obtained by composing an iterative method obtained in Noor et al. [9] with Newton’s method and approximating the first-appeared derivative in the last step by a combination of already evaluated function values. The convergence analysis of o...

In this paper, we study the convergence and almost sure (S, T)−stability of Jungck-Noor type, Jungck-SP type, Jungck-Ishikawa type and Jungck-Mann type random iterative algorithms for some kind of a general contractive type random operators (2.14) in a separable Banach spaces. The Bochner integrability of random fixed point of this kind of random operators, the convergence and almost sure (S, T...

let $c$ be a nonempty closed convex subset of a real hilbert space $h$. let ${s_n}$ and ${t_n}$ be sequences of nonexpansive self-mappings of $c$, where one of them is a strongly nonexpansive sequence. k. aoyama and y. kimura introduced the iteration process $x_{n+1}=beta_nx_n+(1-beta_n)s_n(alpha_nu+(1-alpha_n)t_nx_n)$ for finding the common fixed point of ${s_n}$ and ${t_n}$, where $uin c$ is ...

In this paper, a reliable iterative approach, for solving a wide range of linear and nonlinear Volterra-Fredholm integral equations is established. First the approach considers a discretized form of the integral terms where considering some conditions on the kernel of the integral equation it is proved that solution of the discretized form converges to the exact solution of the problem. Then th...

The purpose of this paper is to study sufficient and necessary conditions for finite-step iterative sequences withmean errors for a finite family of asymptotically quasi-nonexpansive and type mappings in Banach spaces to converge to a common fixed point. The results presented in this paper improve and extend the recent ones announced by GhostDebnath, Liu, Xu and Noor, Chang, Shahzad et al., Sha...