We consider a mean value iteration for a family of functions, which corresponds to the Mann iteration with lim n→∞ α n = 0. We prove convergence results for this iteration when applied to strongly pseudocontractive or strongly accretive maps.

In this paper, we survey the split problem of fixed points two pseudocontractive operators and variational inequalities pseudomonotone in Hilbert spaces. We present a Tseng-type iterative algorithm for solving by using self-adaptive techniques. Under certain assumptions, show that proposed converges weakly to solution problem. An application is included.

in this paper‎, ‎strong convergence theorems of ishikawa type implicit iteration‎ ‎process with errors for a finite family of asymptotically‎ ‎nonexpansive in the intermediate sense and asymptotically‎ ‎quasi-pseudocontractive type mappings in normed linear spaces are‎ ‎established by using a new analytical method‎, ‎which essentially‎ ‎improve and extend some recent results obtained by yang‎ ‎...

for all x ∈ C, p ∈ F T and n ≥ 1. It is clear that if F T is nonempty, then the asymptotically nonexpansive mapping, the asymptotically quasi-nonexpansive mapping, and the generalized quasi-nonexpansive mapping are all the generalized asymptotically quasi-nonexpansive mapping. Recall also that a mapping T : C → C is said to be asymptotically quasi-nonexpasnive in the intermediate sense provided...

and Applied Analysis 3 The aim of this paper is to prove the equivalence of convergent results of above Ishikawa andMann iterations with errors for generalized asymptoticallyΦ-strongly pseudocontractive mappings without bounded range assumptions in uniformly smooth real Banach spaces. For this, we need the following concepts and lemmas. Definition 1.4 see 4 . The mapping T is called generalized...

In this paper we prove an analogue of Banach and Kannan fixed point theorems by generalizing the Lipschitz constat $k$, in generalized Lipschitz mapping on cone metric space over Banach algebra, which are answers for the open problems proposed by Sastry et al, [K. P. R. Sastry, G. A. Naidu, T. Bakeshie, Fixed point theorems in cone metric spaces with Banach algebra cones, Int. J. of Math. Sci. ...

The purpose of this paper is to find of the theoretical results of fixed point theorems for a mixed monotone mapping in a metric space endowed with partially order by using the generalized Kanann type contractivity of assumption. Also, as an application, we prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic bou...