The Krasnoselskii-Mann iteration plays an important role in the approximation of fixed points of nonexpansive operators; it is is known to be weakly convergent in the infinite dimensional setting. In this present paper, we provide a new inexact Krasnoselskii-Mann iteration and prove weak convergence under certain accuracy criteria on the error resulting from the inexactness. We also show strong...

In this paper, we present the convergence of Krasnoselskii Mann iterative process for common fixed points pointwise Lipschitzian evolution family bounded nonlinear operators on a Banach space ℜ .

In this paper, we introduce a Mann-Krasnoselskii algorithm of inertial form for approximating common solution Spit Variational Inclusion Problem (SVIP) and Equilibrium (EP) with paramonotone bifunction in real Hilbert spaces. Motivated by the self-adaptive technique, incorporate technique to accelerate convergence proposed method. Under standard mild assumptions such as monotonicity lower semic...

In this paper, we introduce two iterative schemes by a modified Krasnoselskii-Mann algorithm for finding a common element of the set of solutions of equilibrium problems and the set of fixed points of multivalued nonexpansive mappings in Hilbert space. We prove that the sequence generated by the proposed method converges strongly to a common element of the set of solutions of equilibruim proble...

Let $ H$ be a Hilbert space and $C$ be a closed, convex and nonempty subset of $H$. Let $T:C rightarrow H$ be a non-self and non-expansive mapping. V. Colao and G. Marino with particular choice of the sequence  ${alpha_{n}}$ in Krasonselskii-Mann algorithm, ${x}_{n+1}={alpha}_{n}{x}_{n}+(1-{alpha}_{n})T({x}_{n}),$ proved both weak and strong converging results. In this paper, we generalize thei...