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...

In this paper, the concept of the strongly monotone type mapping is introduced, which contains the strongly monotone mapping and firmly type nonexpansive mapping as special cases. We show the equivalence between the fixed point problem and the complementarity problem of strongly monotone type mapping. Furthermore, it is obtained that an iteration sequence strongly converges to a unique solution...

Correspondence: [email protected] Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand Abstract In this article, we introduce a new mapping generated by infinite family of nonexpansive mapping and infinite real numbers. By means of the new mapping, we prove a strong convergence theorem for finding a common element of the se...

Let X be a real Banach space and let C be a nonempty closed convex subset of X. A selfmapping T : C → C is said to be nonexpansive if ‖Tx−Ty‖ ≤ ‖x−y‖, for all x, y ∈ C.A point x ∈ C is a fixed point of T provided Tx x. Denote by Fix T the set of fixed points of T ; that is, Fix T {x ∈ C : Tx x}. It is assumed throughout this paper that T is a nonexpansive mapping such that Fix T / ∅. Constructi...

Let K be a nonempty closed convex subset of a real Banach space E which has a uniformly Gâteaux differentiable norm. Assume that K is a sunny nonexpansive retract of E with Q as the sunny nonexpansive retraction. Let Ti : K → E, i = 1, 2, · · · , N be a family of nonexpansive mappings which are weakly inward with F = ⋂N i=1 F (Ti) 6= ∅. Let f : K → K be a fixed contractive mapping. For given x0...

Kohlenbach and Leuştean have shown in 2010 that any asymptotically nonexpansive self-mapping of a bounded nonempty UCW-hyperbolic space has fixed point. In this paper, we adapt construction due to Moloney order provide sequence converges strongly such

Our concern is with the Lipschitz constant of T; i.e. with the constant K such that || J # — 7 j | | ^i£||#—;y|| for all x, y in X. In particular, we wish to determine under what conditions on the space X the mapping T will be nonexpansive, i.e. K = l. T is a special case of a proximity mapping defined by a convex set in a normed vector space, i.e. a mapping which assigns to each point of X, th...