We introduce a new hybrid iterative algorithm for finding a common element of the set of fixed points of hemirelatively nonexpansive mappings and the set of solutions of an equilibrium problem and for finding a common element of the set of zero points of maximal monotone operators and the set of solutions of an equilibrium problem in a Banach space. Using this theorem, we obtain three new resul...

We introduce a new iterative algorithm for finding a common element of the solution set of the variational inequality problem for a continuous monotone mapping, the zero point set of a maximal monotone operator, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the sequence generated by the proposed algorithm to a commo...

n this paper , we propose a generalized iterative method forfinding a common element of the set of fixed points of a singlenonexpannsive mapping and the set of solutions of two variationalinequalities with inverse strongly monotone mappings and strictlypseudo-contractive of Browder-Petryshyn type mapping. Our resultsimprove and extend the results announced by many others.

n this paper , we propose a generalized iterative method forfinding a common element of the set of fixed points of a singlenonexpannsive mapping and the set of solutions of two variationalinequalities with inverse strongly monotone mappings and strictlypseudo-contractive of browder-petryshyn type mapping. our resultsimprove and extend the results announced by many others.

We give the weakest constraint qualification known to us that ensures the maximal monotonicity of the operator A∗ ◦ T ◦A when A is a linear continuous mapping between two reflexive Banach spaces and T is a maximal monotone operator. As a special case we get the weakest constraint qualification that ensures the maximal monotonicity of the sum of two maximal monotone operators on a reflexive Bana...

and Applied Analysis 3 2. Preliminaries Now, we list some of the knowledge we need in the sequel. Let X be a real Banach space with a strictly convex dual space X∗. We use ·, · to denote the generalized duality pairing between X and X∗. We use “→ ” to denote strong convergence. Let “X ↪→ Y” denote the space X embedded continuously in space Y . For any subset G of X, we denote by intG its interi...

Let Y be a Banach space, Y* its conjugate space, X a weak*-dense closed subspace of Y* with the induced norm. We denote the pairing between x in X and ƒ in 7 by (y, x). If T is a mapping from X into 2 F , T is said to be monotone if for each pair of elements [x9 y] and [u, w] of G(T)9 the graph of T, we have (y—w, x—w)^0. Tis said to be maximal monotone from X to 2 F if Tis monotone and maximal...