In this paper, we introduce a new class of set-valued mappings which is called MD-type mappings. This class of mappings is a set-valued case of a class of the D-type mappings. The class of D-type mappings is a generalization of nonexpansive mappings that recently introduced by Kaewkhao and Sokhuma. The class of MD-type mappings includes upper semi-continuous Suzuki type mappings, upper semi-con...

We show some stability and convergence theorems of the modified Ishikawa iterative sequence with errors for a strongly successively pseudocontractive and strictly asymptotically pseudocontractive mapping in a real Banach space. Additionally, we prove that if T is a uniformly Lipschitzian strongly accretive mapping, the modified Ishikawa iteration sequence with errors converges strongly to the u...

The purpose of this paper is to propose a compositeiterative scheme for approximating a common solution for a finitefamily of m-accretive operators in a strictly convex Banach spacehaving a uniformly Gateaux differentiable norm. As a consequence,the strong convergence of the scheme for a common fixed point ofa finite family of pseudocontractive mappings is also obtained.

Let E be a real Banach space, {Ti}i=1 be a finite family of continuous pseudocontractive self mappings of E and G : E → E be a mapping which is both δ -strongly accretive and λ -strictly pseudocontractive of Browder-Petryshyn type such that δ + λ 1 . We propose a new implicit iteration scheme with perturbed mapping G for the approximation of common fixed points of {Ti}i=1 . For an arbitrary ini...

In this paper, we construct a new iterative scheme by hybrid projection method and prove strong convergence theorems for approximation of a common element of set of common fixed points of an infinite family of asymptotically quasi-φ-nonexpansive mappings, set of solutions to a variational inequality problem and set of common solutions to a system of generalized mixed equilibrium problems in a u...

Keywords: Implicit iterative algorithm Asymptotically quasi-nonexpansive mappings Common fixed point Convex metric space a b s t r a c t In this paper, we consider an implicit iteration process to approximate the common fixed points of two finite families of asymptotically quasi-nonexpansive mappings in convex metric spaces. As a consequence of our result, we obtain some related convergence the...

In this paper, we proposed a new two-step iteration scheme of hybrid mixed type for two asymptotically nonexpansive self mappings and two total asymptotically nonexpansive non-self mappings and establish some weak convergence theorems for mentioned scheme and mappings in the setting of uniformly convex Banach spaces. Our results extend and generalize several results from the current existing li...

The aim of this article is to establish some strong convergence theorems of three-step iteration process with errors for approximating common fixed point for generalized asymptotically quasi-nonexpansive mappings and also establish a weak convergence theorem by using Opial’s [11] condition for said iteration scheme and mappings in the framework of Banach spaces. The results presented in this pa...