zero point problems of the sum of two monotone mappings and fixed point problems of a strictly pseudocontractive mapping are investigated‎. ‎a strong convergence theorem for the common solutions of the problems is established in the framework of hilbert spaces‎.

and Applied Analysis 3 It is easy to see that a quasi-nonexpansive mapping is an asymptotically quasi-nonexpansive mapping with the sequence {1}. T is said to be asymptotically nonexpansive in the intermediate sense if and only if it is continuous, and the following inequality holds: lim sup n→∞ sup x,y∈C (∥ ∥Tx − Tny∥∥ − ∥∥x − y∥∥) ≤ 0. 2.6 T is said to be asymptotically quasi-nonexpansive in ...

Let E be a real q-uniformly smooth Banach space which is also uniformly convex and K be a nonempty, closed and convex subset of E. We obtain a weak convergence theorem of the explicit averaging cyclic algorithm for a finite family of asymptotically strictly pseudocontractive mappings of K under suitable control conditions, and elicit a necessary and sufficient condition that guarantees strong c...

Let E be a real uniformly convex Banach space which has the Fréchet differentiable norm, and K a nonempty, closed, and convex subset of E. Let T : K ® K be an asymptotically -strictly pseudocontractive mapping with a nonempty fixed point set. We prove that (I T) is demiclosed at 0 and obtain a weak convergence theorem of the modified Mann’s algorithm for T under suitable control conditions. Mor...