Let E be a real reflexive and strictly convex Banach space which has a uniformly Gâteaux differentiable norm and let C be a closed convex nonempty subset of E. Strong convergence theorems for approximation of a common zero of a countably infinite family of m-accretive mappings from C to E are proved. Consequently, we obtained strong convergence theorems for a countably infinite family of pseudo...

In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a general variational inequality problem for finite inversestrongly accretive mappings and the set of common fixed points of a countable family of strict pseudocontractive mappings in a Banach space. We obtain a strong convergence theorem under some suitable conditions. Our results impr...

In this paper, we aimed to introduce a new viscosity-type approximation method for finding the common fixed point of class quasi-pseudocontractive mapping and system monotone inclusion problems in CAT(0) spaces. We proved some fixed-point properties concerning spaces, which is more general than many other mappings such as nonexpansive, quasi-nonexpansive, pseudocontractive demicontractive have ...

The aim of this paper is to introduce a viscosity iterative algorithm for the implicit midpoint rule of nonexpansive mappings in uniformly smooth spaces. Under some appropriate conditions on the parameters, we prove some strong convergence theorems. As applications, we apply our main results to solving fixed point problems of strict pseudocontractive mappings, variational inequality problems in...

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 ...

We prove path convergence theorems and introduce a new iterative sequence for a countably infinite family of m-accretive mappings and prove strong convergence of the sequence to a common zero of these operators in uniformly convex real Banach space. Consequently, we obtain strong convergence theorems for a countably infinite family of pseudocontractive mappings. Our theorems extend and improve ...

The shrinking projection method has gained more and more attention as a powerful tool for the approximation of a fixed point of nonlinear mappings. In this paper, we introduce a new shrinking projection method for the approximation of fixed points of a family of pseudocontractive mappings in a Hilbert space. Using this method, we also deal with the problem of finding a common zero of a family o...

We introduce an iterative algorithm for finding a common element of the set of fixed points for an infinite family of nonexpansive mappings, the set of solutions of the variational inequalities for a family of α-inverse-strongly monotone mappings and the set of solutions of a system of equilibrium problems in a Hilbert space. We prove the strong convergence of the proposed iterative algorithm t...