In this paper, we studied maximal monotonicity of type FPV for sum of two maximal monotone operators of type FPV and the obtained results improve and complete the corresponding results of this filed.

The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical Rockafellar’s constraint qualification holds. In this paper, we establish the maximal monotonicity of A+ B provided that A and B are maximally monotone operators such that star(domA)∩ int domB 6= ∅, and A is of type (FPV). We sh...

let $x$ be a reflexive banach space, $t:xto x$ be a nonexpansive mapping with $c=fix(t)neqemptyset$ and $f:xto x$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. in this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences t...

Maximal monotone operators on a Banach space into its dual can be represented by convex functions bounded below by the duality product. It is natural to ask under which conditions a convex function represents a maximal monotone operator. A satisfactory answer, in the context of reflexive Banach spaces, has been obtained some years ago. Recently, a partial result on non-reflexive Banach spaces w...

We address the generalized Nash equilibrium seeking problem for noncooperative agents playing non-strictly monotone aggregative games with affine coupling constraints. First, we use operator theory to characterize the generalized Nash equilibria of the game as the zeros of a monotone setvalued operator. Then, we massage the Douglas–Rachford splitting to solve the monotone inclusion problem and ...

We prove strong convergence theorems for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a hemirelatively nonexpansive mapping in a Banach space by using monotone hybrid iteration method. By using these results, we obtain new convergence results for resolvents of maximal monotone operators and hemirelatively nonexpansive mappings in a Ban...