Let C be a closed convex subset of a real Hilbert space H . Let A be an inverse-strongly monotone mapping of C into H and let B be a maximal monotone operator on H such that the domain of B is included in C . We introduce two iteration schemes of finding a point of (A+B)−10, where (A+B)−10 is the set of zero points of A+B. Then, we prove two strong convergence theorems of Halpern’s type in a Hi...

The purpose of this paper is to study the strong convergence of a hybrid iterative scheme for finding a common element of the set of a general system of variational inequalities for α-inversestrongly monotone mapping and relaxed (c,d)cocoercive mapping, the set of solutions of a mixed equilibrium problem and the set of common fixed points of a finite family of nonexpansive mappings in a real Hi...

is not properly contained in the graph of any other monotone mapping. It is known that T is maximal iff R(I+rT ) = H for every r > 0, where R(I+rT ) = ∪ {z+rTz : z ∈ H,Tz ̸= ∅}. Monotone operators have proven to be a key class of objects in modern Optimization and Analysis; see, e.g., the books [1-7] and the references therein. Let us consider the zero point problem for a monotone operator T on ...

This paper is concerned with some new projection methods for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. First, we propose the projected reflected gradient algorithm with a constant stepsize. It is similar to the projected gradient method, namely, the method requires only one projection onto the feasible set and only one value of the ...

A regressive function (also called a regression or contractwe mapping) on a partial order P is a function (T mapping P to itself such that o(x) < x. A monotone k-chain for CJ is a k-chain on which u is order-preserving; i.e., a chain x1 < ... <XL such that a(.~, ) d ... < a(xk). Let P,be the poset of integer intervals {i, i + 1, , m} contained in { 1,2, . . . . n}, ordered by inclusion. Let f(k...

As the capacity to summarize of the preference map diminishes with the number of consumers (the number of axes to interpret increases), a non-metric PCA is sometimes used to reduce the number of necessary axes. The non-metric PCA consists of a monotone transform of the data so that the variability explained by the k (k=2 or 3) first axes is maximized. This transform implies that we consider the...

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...

Using the concept of a mixed g-monotone mapping, we prove some coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings in partially ordered complete quasi-metric spaces with a Q-function q. The presented theorems are generalizations of the recent coupled fixed point theorems due to Bhaskar and Lakshmikantham 2006 , Lakshmikantham and Ćirić 2009 and many ot...