The purpose of this paper is to study and give the necessary andsufficient condition of strong convergence of the multi-step iterative algorithmwith errors for a finite family of generalized asymptotically quasi-nonexpansivemappings to converge to common fixed points in Banach spaces. Our resultsextend and improve some recent results in the literature (see, e.g. [2, 3, 5, 6, 7, 8,11, 14, 19]).

The purpose of this paper is to introduce a new hybrid extragradient iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and satisfying solutions of the split feasibility problem (SFP) and systems of equilibrium problem (SEP) in Hilbert spaces. We prove that the sequence generated by the proposed algorithm converge strongly to a common elem...

We introduce the classes of nearly contraction mappings and nearly asymptotically nonexpansive mappings. The class of nearly contraction mappings includes the class of contraction mappings, but the class of nearly asymptotically nonexpansive mappings contains the class of asymptotically nonexpansive mappings and is contained in the class of mappings of asymptotically nonexpansive type. We study...

begin{abstract} in this paper, we prove some strong and weak convergence of three step random iterative scheme with errors to common random fixed points of three asymptotically nonexpansive nonself random mappings in a real uniformly convex separable banach space. end{abstract}

where {an} is a sequence in [0,1] and {un} a sequence in E satisfying ∑∞ n=1‖un‖<∞, is known as Mann iterative scheme with errors. In 1999, Huang [2] studied the above schemes for asymptotically nonexpansive mappings. Recall that a mapping T : C → C is asymptotically nonexpansive if there is a sequence {kn} ⊂ [1,∞) with limn→∞kn = 1 and ‖Tnx−Tny‖ ≤ kn‖x−y‖ for all x,y ∈ C and for all n∈N, where...

In this paper, we establish the existence of a fixed point for generalized nonexpansive multivalued mappings in hyperbolic spaces and we prove some [Formula: see text]-convergence and strong convergence theorems for the iterative scheme proposed by Chang et al. (Appl Math Comp 249:535-540, 2014) to approximate a fixed point for generalized nonexpansive multivalued mapping under suitable conditi...

and Applied Analysis 3 Recall that the Bregman projection [13] of x ∈ int domf onto the nonempty, closed, and convex subset C of domf is the necessarily unique vector projf C (x) ∈ C satisfying D f (projf C (x) , x) = inf{D f (y, x) : y ∈ C} . (12) Let f : E → (−∞, +∞] be a convex and Gâteaux differentiable function. The function f is said to be totally convex at x ∈ int domf if its modulus of ...