[PDF] Top 20 A regularization method for treating zero points of the sum of two monotone operators

... be monotone iff, for all x, y ∈ H, f ∈ Bx and g ∈ By imply x – y, f – g > ...the zero point of B. A monotone mapping B : H ⇒ H is maximal iff the graph Graph(B) of B is not properly contained in the ... See full document

... the regularization method for solving the variational inclusion problem of the sum of two monotone operators in Hilbert ... See full document

... of monotone operators has appeared as a powerful and effective tool for studying a wide class of problems arising in different branches of social, engineering, and pure sciences in a unified and general ... See full document

... and zero points of the sum of two monotone operators based on a viscosity splitting ...the two problems are established in Hilbert ... See full document

... Many nonlinear problems arising in applied areas such as image recovery, signal process- ing, and machine learning are mathematically modeled as a nonlinear operator equation and this operator is decomposed as the ... See full document

... studied zero point problems of the sum of two monotone map- pings and fixed point problems of a nonexpansive mapping based on the following iterative ... See full document

... projection method for approximating a common element of the set of zeroes of a finite family of maximal monotone operators and the set of common solutions to a system of generalized equilibrium ... See full document

... therein. Regularization methods recently have been investigated for treating zero points of monotone operators; for [–] and the references ...finding zero points ... See full document

... projection method and its different kinds including the Wiener-Hopf equations can not be expanded and improved to solve mixed equilibrium-variational inequalities due to the nature of the ...present two ... See full document

... the regularization algorithm, is proved in Section ...the zero points of the sum of two operators are pre- sented in Section ... See full document

... Using the notion of compatible mappings in the setting of a partially ordered metric space, we prove the existence and uniqueness of coupled coincidence points involving a (j, ψ)-contractive condition for a ... See full document

... Theorem . Let (X, ) be a partially ordered set and suppose there is a partial metric p on X such that (X, d) is a complete partial metric space. Let g : X → X and F : X × X → X be a mapping having the mixed ... See full document

... Theorem 2.2. Let P be a normal cone in E, and A : P × P × P → P a mixed monotone operator. Let B : E → E be sublinear. Assume that for all a < t < b, there exist two positive-valued functions τ (t), ... See full document

... whose solutions correspond to the equilibrium points of the system (.). Consequently, considerable research efforts have been devoted, especially within the past  years or so, to methods for finding approximate ... See full document

... Suppose that (E, · ) is a Banach space and θ is the zero element of E. Recall that a non- empty closed convex set P ⊂ E is a cone if it satisfies () x ∈ P, λ ≥  ⇒ λx ∈ P; () x ∈ P, –x ∈ P ⇒ x = θ . The Banach ... See full document

... positive sum game occurs when no one wins at someone else's expense – indeed the sum of positives and negatives (wins and losses) is ...with zero sum ...positive- sum game viewpoint, ... See full document

... non zero-sum n players game by an n + 1 players zero-sum ...the sum of the payoffs of the n players, then the game with n + 1 players, n players in the main game and the n + 1-th ... See full document

... be monotone of x − y, x ∗ − y ∗ ≥ 0, for all x, x ∗ , y, y ∗ ∈ A. A monotone operator A ⊂ E × E ∗ is said to be maximal monotone if its graph is not properly contained in the graph of any other ... See full document

... Motivated by the above work, in this paper, we shall use the properties of reproduc- ing cones to establish some fixed point theorems for multi-valued monotone and mixed monotone operators. Compared ... See full document

... finding zero points, for instance, evolution equations, complemen- tarity problems, mini-max problems, variational inequalities and optimization ...finding zero points of the subdifferential ... See full document