A composite explicit iterative process with a viscosity method for Lipschitzian semigroup in a smooth Banach space

a composite explicit iterative process with a viscosity method for lipschitzian semigroup in a smooth banach space

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Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert Space

Let C be nonempty closed convex subset of real Hilbert space H. Consider C a nonexpansive semigroup I {T s : s ≥ 0}with a common fixed point, a contraction f with coefficient 0 < α < 1, and a strongly positive linear bounded operator A with coefficient γ > 0. Let 0 < γ < γ/α. It is proved that the sequence {xn} generated iteratively by xn I − αnA 1/tn ∫ tn 0 T s ynds αnγf xn , yn I − βnA xn βnγ...

A General Iterative Method for a Nonexpansive Semigroup in Banach Spaces with Gauge Functions

Viscosity Approximation of Common Fixed Points for L-Lipschitzian Semigroup of Pseudocontractive Mappings in Banach Spaces

We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach...

Approximating Common Fixed Points of Lipschitzian Semigroup in Smooth Banach Spaces

Recommended by Mohamed Khamsi Let S be a left amenable semigroup, let S {T s : s ∈ S} be a representation of S as Lipschitzian mappings from a nonempty compact convex subset C of a smooth Banach space E into C with a uniform Lipschitzian condition, let {μn} be a strongly left regular sequence of means defined on an S-stable subspace of l∞ S , let f be a contraction on C, and let {αn}, {βn}, and...

Iterative Process for an α- Nonexpansive Mapping and a Mapping Satisfying Condition(C) in a Convex Metric Space

We construct one-step iterative process for an α- nonexpansive mapping and a mapping satisfying condition (C) in the framework of a convex metric space. We study △-convergence and strong convergence of the iterative process to the common fixed point of the mappings. Our results are new and are valid in hyperbolic spaces, CAT(0) spaces, Banach spaces and Hilbert spaces, simultaneously.