We introduce a concept of weak Bregman relatively nonexpansive mapping which is distinct from Bregman relatively nonexpansive mapping. By using projection techniques, we construct several modification of Mann type iterative algorithms with errors and Halpern-type iterative algorithms with errors to find fixed points of weak Bregman relatively nonexpansive mappings and Bregman relatively nonexpa...

Abstract This paper first introduces a new iterative method for weak and strong convergence theorem to demonstrate the estimation potential fixed point of cutter finite general split feasibility problem. Consequently, set points quasi-nonexpansive mapping problem, constrained minimization problems are proved using our main results. Finally, we give two numerical examples advocate

In this paper, an iterative scheme for finding common solutions of the set fixed points a pair asymptotically quasi-nonexpansive mapping and minimizers minimization problem is constructed. Using idea jointly demicloseness principle, strong convergence results are achieved without imposing any compactness condition on space or operator. Our improve, extend generalize many important in literature.

* Correspondence: [email protected] College of Science, Civil Aviation University of China, Tianjin 300300, China Abstract Iterative algorithms have been extensively studied over the class of nonexpansive mappings in Hilbert spaces. Recall that nonexpansive mappings belong to quasinonexpansive mappings. The aim of this article is expanding the general approximation method proposed by Marino ...

Mean nonexpansive mappings were first introduced in 2007 by Goebel and Japón Pineda and advances have been made by several authors toward understanding their fixed point properties in various contexts. For any given mean nonexpansive mapping of a Banach space, many of the positive results have been derived from knowing that a certain average of some iterates of the mapping is nonexpansive. Howe...

and Applied Analysis 3 Let E be a real Banach space and let C be a nonempty closed and convex subset of E, and A : C → E∗ be a mapping. The classical variational inequality problem for a mapping A is to find x∗ ∈ C such that 〈 Ax∗, y − x∗〉 ≥ 0, ∀y ∈ C. 1.7 The set of solutions of 1.4 is denoted by VI A,C . Recall that A is called i monotone if 〈 Ax −Ay, x − y〉 ≥ 0, ∀x, y ∈ C, 1.8 ii an α-invers...

In this paper, we extend the results of Inprasit and Wattanataweekul [7] to the class of asymptotically quasi-nonexpansive nonself-mappings in the intermediate sense. We prove some strong convergence theorems for asymptotically quasi-nonexpansive nonself-mappings in the intermediate sense using a three-step iterative method for finding a common element of the set of solutions of a generalized m...

There are two important connections between the classes of nonexpansive and of accretive mappings which give rise to a strong connection between the fixed point theory of nonexpansive mappings and the mapping theory of accretive maps. These are: (1) If U is a nonexpansive mapping of D(U) into X, and if we set T — I--U, D(T)=D(U), then T is an accretive mapping of D{T) into X. (2) If { U(i)f t^O...

It is shown that any A-firmly, 0 < A < 1 , nonexpansive mapping T: C —> C has a fixed point in C whenever C is a finite union of nonempty, bounded, closed convex subsets of a uniformly convex Banach space. Let C be a nonempty subset of a Banach space X, and let X £ (0, 1). Then a mapping T: C —> X is said to be X-firmly nonexpansive if (1) \\Tx Ty\\ < ||(1 X)(x y)+X(Tx Ty)\\ for all x, y £ C. I...