In this paper we study the hybrid iterative scheme to find a common element of a set of solutions of generalized mixed equilibrium problem, a set of common fixed points of finite family of weak relatively nonexpansive mapping, and null spaces of finite family of γ-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. Our results extend, improve and g...

In this paper, we introduce a modified CQ iterative scheme for finding a common element of the set of solutions of an equilibrium problem, the set of fixed points of an infinite family of nonexpansive mappings and the set of the variational inequality for an α-inverse strongly monotone mapping in a Hilbert space. We obtain a strong convergence theorem for three sequences generated by this proce...

We introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem, the set of solutions of the variational inequality for a β-inversestrongly monotone mapping, and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Cesàro mean approximation method. We prove that the sequenc...

and Applied Analysis 3 Let C be a nonempty closed convex subset of a real Hilbert space H. Recall that a mapping A : C → H is called α-inverse strongly monotone if there exists a positive real number α such that 〈Ax − Ay, x − y〉 ≥ α‖Ax −Ay‖, for all x, y ∈ C. It is clear that any αinverse strongly monotone mapping is monotone and 1/α-Lipschitz continuous. Let f : C → H be a ρ-contraction; that ...

This paper deals with global convergence to equilibria, and in particular Hirsch’s generic convergence theorem for strongly monotone systems, for singular perturbations of monotone systems.

Let X be a real reflexive Banach space and A: X — 2A a maximal monotone mapping such that the graph G(A) of A is weaklyclosed in X X X and 0 £/4(0). Also, let T: X — 2A be a quasi-bounded coercive mapping of type (M) such that the effective domain D(T) of T contains a dense linear subspace X of X. Then it is shown that for each * f I co e X there exists a u e X such that co e Au + Tu and the su...

We study several properties of a homotopy solution mapping, based on Zhang and Zhang's homotopy formulation, for continuous nonlinear complementarity problems with such non-monotone maps as quasi-monotone, E 0-, and exceptional regular functions. For these classes of complementarity problems, we establish several suucient conditions to assure the nonemptyness and boundedness of the homotopy sol...

Let $E$ be a uniformly smooth and convex real Banach space $E^*$ its dual space. Suppose $A : E\rightarrow E^*$ is bounded, strongly monotone satisfies the range condition such that $A^{-1}(0)\neq \emptyset$. Inspired by Alber [2], we introduce Lyapunov functions use new geometric properties of spaces to show strong convergence an iterative algorithm solution $Ax=0$.

Distributed computation follows the models of discrete structures in combinatorial forms. In higher-dimensions, the simplex structures of topological spaces as well as homology are employed to model and analyze distributed asynchronous computations. However, the monotone spaces are the general forms of topological spaces and can be effectively employed to analyze distributed computation. This p...