In this paper. We introduce a general iterative method for the family of mappings and prove the strong convergence of the new iterative scheme in Banach space. The new iterative method includes the iterative scheme of Khan and Domlo and Fukhar-ud-din [Common fixed points Noor iteration for a finite family of asymptotically quasinonexpansive mappings in Banach spaces. J. Math. Anal. Appl. 341 (2...

The notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $CAT(0)$ space, where the curvature is bounded from above by zero. In fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. In this paper, w...

In this paper, we are concerned with the study of a multi-step iterative scheme with errors insolving a finite family of asymptotically quasinonexpansive self-mappings. We approximate the common fixed points of a finite family of asymptotically quasi-nonexpansive self-mappings by convergence of the scheme in a uniformly convex Banach space. Our results extend and improve some recent results, Q....

we prove a strong convergence result for a sequence generated by halpern's type iteration for approximating a common fixed point of a countable family of quasi-lipschitzian mappings in a real hilbert space. consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

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 ...

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 ...