and Applied Analysis 3 It is clear that 1.7 is equivalent to 〈 Sx − Sy, x − y ≤ ∥x − y∥2, ∀x, y ∈ C. 1.8 The class of κ-strict pseudocontractions which was introduced by Browder and Petryshyn 17 in 1967 has been considered by many authors. It is easy to see that the class of strict pseudocontractions falls into the one between the class of nonexpansive mappings and the class of pseudocontractio...

Throughout this paper, we denote by N, Z, Q and R the sets of all positive integers, all integers, all rational numbers and all real numbers, respectively. We put R+ = [0,∞)n and ej = (0, 0, · · · , 0, 0, (j) 1 , 0, 0, · · · , 0) ∈ R for j ∈ N with 1 ≤ j ≤ n. Let C be a subset of a Banach space E, and let T be a nonexpansive mapping on C, i.e., ‖Tx−Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. We know that T ...

Objectives: The objective of the paper is to find solutions variational inequality problems via concept common fixed point a sequence nearly nonexpansive mappings. Methods: present work uses three step iterative algorithm get problems. Findings: By applying algorithm, problem has been obtained. Novelty: In work, specific deployed solution. Furthermore, Matlab programming utilised eastablish acc...

Let X and Y be real Banach spaces, ƒ a mapping of X into 2, y0 an element of Y It is our object in the present discussion to present a new existence theory for solutions of the equation y0£f(x) which extends, sharpens, and simplifies the corresponding theory for X — Y and ƒ hypermaximal accretive. This new existence theory is founded in a very basic way upon the fixed point theory of self-mappi...

Let C be a subset of a Banach space E. A mapping T : C → E is nonexpansive if ‖Tx − Ty‖ ≤ ‖x − y‖ for all x, y ∈ C. In 1965, it was proved independently by Browder 1 , Göhde 2 , and Kirk 3 that if C is a bounded closed convex subset of a Hilbert space and T : C → C is nonexpansive, then T has a fixed point. Combining the results above, Ray 4 obtained the following interesting result see 5 for a...

We use a hybrid iterative method to find a common element of the set of fixed points of an infinite family of Lipschitzian quasi-nonexpansive mappings, the set of solutions of the general system of the variational inequality and the set of solutions of the generalized mixed equilibrium problem in real Hilbert spaces. We also show that our main strong convergence theorem for finding that common ...