Tae-Hwa Kim and Hong-Kun Xu [Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Analysis 64(2006)1140-1152 ] proved the strong convergence theorems of modified Mann iterations for asymptotically nonexpansive mappings and semigroups on bounded subset C of a Hilbert space by the CQ iteration method. The purpose of this paper is to mod...

In this paper, we introduce an iterative process which converges strongly to a common element of solutions of variational inequality problems for γ-inverse strongly monotone mappings and common fixed points of a countable family of total quasi-φ-asymptotically nonexpansive nonself mappings, and hence obtain related convergence theorems in Banach spaces. Mathematics Subject Classification: 47H09...

In this paper, we provide existence and convergence theorems of common fixed points for left (or right) reversible semitopological semigroups of total asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper extend and improve some recent results announced by other authors.

and Applied Analysis 3 Let {xn} be a bounded sequence in a CAT 0 space X. For x ∈ X, one sets r x, {xn} lim sup n→∞ d x, xn . 2.5 The asymptotic radius r {xn} of {xn} is given by r {xn} inf x∈X {r x, {xn} }, 2.6 the asymptotic radius rC {xn} of {xn}with respect to C ⊂ X is given by rC {xn} inf x∈C {r x, {xn} }, 2.7 the asymptotic center A {xn} of {xn} is the set A {xn} {x ∈ X : r x, {xn} r {xn}...

In this paper, we introduce a class of total quasi-φ-asymptotically nonexpansive nonself mappings which contain several kinds of mappings as its special cases, and obtain some strong convergence theorems for this type of mappings in Banach spaces under some mild control conditions. The results presented in this paper improve and extend some recent corresponding results.

We prove strong convergence theorem for infinite family of uniformly L−Lipschitzian total quasi-φ-asymptotically nonexpansive multi-valued mappings using a generalized f−projection operator in a real uniformly convex and uniformly smooth Banach space. The result presented in this paper improve and unify important recent results announced by many authors.