and Applied Analysis 3 space X is embedded compactly in space Y and “X ↪→ Y ′′ denote that space X is embedded continuously in space Y. A mapping T : D T X → X∗ is said to be hemicontinuous on X if w − limt→ 0T x ty Tx, for any x, y ∈ X. Let J denote the duality mapping from X into 2 ∗ defined by J x { f ∈ X∗ : (x, f) ‖x‖ · ∥∥f∥∥,∥∥f∥∥ ‖x‖}, x ∈ X, 1.5 where ·, · denotes the generalized duality...

Symmetries play an important role in the dynamics of physical systems. As example, quantum physics and microworld are basis symmetry principles. These problems reduced to solving inequalities general. That is why this article, we study numerical approximation solutions variational inequality involving quasimonotone operators infinite-dimensional real Hilbert space. We prove that iterative seque...

Recently, we systematically studied the basic theory of Bregman circumcenters in another paper. In this work, aim to apply optimization algorithms. Here, propose forward monotonicity which is a generalization powerful Fejér and show weak convergence result monotone sequence. We also naturally introduce circumcenter mappings associated with finite set operators. Then provide sufficient condition...

Enlargements have proven to be useful tools for studying maximally monotone mappings. It is therefore natural to ask in which cases the enlargement does not change the original mapping. Svaiter has recently characterized non-enlargeable operators in reflexive Banach spaces and has also given some partial results in the nonreflexive case. In the present paper, we provide another characterization...

We introduce a new composite iterative scheme by the viscosity approximation method for nonexpansive mappings andmonotone mappings in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of set of fixed points of nonexpansive mapping and the set of solutions of variational inequality for an inversestrongly monotone mappings, whic...

Each lower semi-continuous proper convex function f on a Banach space E defines a certain multivalued mapping of from E to E* called the subdifferential of f. It is shown here that the mappings arising this way are precisely the ones whose graphs are maximal "cyclically monotone" relations on Ex E*, and that each of these is also a maximal monotone relation. Furthermore, it is proved that of de...

We introduce an iterative method for finding a common element of the set of common fixed points of a countable family of nonexpansivemappings, the set of solutions of a variational inclusion with set-valued maximal monotone mapping, and inverse strongly monotone mappings and the set of solutions of an equilibrium problem in Hilbert spaces. Under suitable conditions, some strong convergence theo...

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 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...

Let Rn be the n-dimensional Euclidean space, T : D(T ) ⊆ Rn → 2R n a maximal monotone mapping, and Ω ⊂ Rn an open bounded subset such that Ω ∩ D(T ) 6= ∅ and assume 0 6∈ T (∂Ω ∩ D(T )). In this note we show an easy way to define the topological degree deg(T ,Ω ∩ D(T ), 0) of T on Ω ∩ D(T ) as the limit of the classical Brouwer degree deg(Tλ,Ω, 0) as λ → 0; here Tλ is the Yosida approximation of...