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A strong convergence result for systems of nonlinear operator equations involving total asymptotically nonexpansive mappings in uniformly convex Banach spaces

Abdelhakim A. A.

Silesian Journal of Pure and Applied Mathematics

2016

Vol. 6, iss. 1

27--48

We prove the strong convergence of an implicit iterative procedure to a solution of a system of nonlinear operator equations involving total asymptotically nonexpansive operators in uniformly convex Banach spaces.

Approximating common random fixed point for two finite families of asymptotically nonexpansive random mappings

Rashwan R. A., Albaqeri D. M.

Fasciculi Mathematici

2014

Nr 53

129--148

The aim of this paper is to study weak and strong convergence of an implicit random iterative process with errors to a common random fixed point of two finite families of asymptotically nonexpansive random mappings in a uniformly convex separable Banach space.

Strong convergence of implicit iteration processes for nonexpansive semigroups in Banach spaces

Kozlowski W. M.

Commentationes Mathematicae

2014

Vol 54, No. 2

203--208

Let C be a convex compact subset of a uniformly convex Banach space. Let {Tt}t≥0 be a strongly-continuous nonexpansive semigroup on C. Consider the iterative process defined by the sequence of equations xk+1=ckTtk+1(xk+1)+(1−ck)xk. We prove that, under certain conditions on {ck} and {tk}, the sequence {xk}∞n=1 converges strongly to a common fixed point of the semigroup {Tt}t≥0. There are known results on convergence of such iterative processes for nonexpansive semigroups in Hilbert spaces and Banach spaces with the Opial property, and also weak convergence results in Banach spaces that are simultaneously uniformly convex and uniformly smooth. In this paper, we do not assume the Opial property or uniform smoothness of the norm.