and Applied Analysis 3 T is said to be an asymptotically strict pseudocontraction in the intermediate sense if there exists a sequence {kn} ⊂ 1,∞ with kn → 1 as n → ∞ and a constant κ ∈ 0, 1 such that lim sup n→∞ sup x,y∈C (∥ ∥Tx − Tny∥∥2 − kn ∥ ∥x − y∥∥2 − κ∥∥ I − T x − I − T y∥∥2 ) ≤ 0. 1.9 For such a case, T is also said to be an asymptotically κ-strict pseudocontraction in the intermediate ...

the purpose of this paper is to study the strong convergence of an implicit iteration process with errors to a common fixed point for a finite family of asymptotically pseudocontractive mappings and nonexpansive mappings in normed linear spaces. the results in this paper improve and extend the corresponding results of xu and ori, zhou and chang, sun, yang and yu in some aspects.

We introduce a new iterative scheme by modifying Mann’s iteration method to find a common element for the set of common fixed points of an infinite family of asymptotically strictly pseudocontractive mappings in the intermediate sense, the set of solutions of the cocoercive quasivariational inclusions problems, and the set of solutions of the mixed equilibrium problems in Hilbert spaces. The st...

In this paper, we establish a weak convergence theorem and some strong convergence theorems of an explicit iteration process for a finite family of strictly asymptotically pseudo-contractive mappings in the intermediate sense and also establish a strong convergence theorem by a new hybrid method for above said iteration scheme and mappings in the setting of Hilbert spaces. AMS Mathematics Subje...

The asymptotically nonexpansive mappings have been introduced by Goebel and Kirk in 1972. Since then, a large number of authors have studied the weak and strong convergence problems of the iterative algorithms for such a class of mappings. It is well known that the asymptotically nonexpansive mappings is a proper subclass of the class of asymptotically pseudocontractive mappings. In the present...