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.

Let H be a real Hilbert space. A mapping A : D(A) ⊆ H → H is said to be monotone if ⟨Ax − Ay, x − y⟩ ≥ 0 for every x, y ∈ D(A). A is called maximal monotone if it is monotone and the R(I + rA) = H, the range of (I + rA), for each r > 0, where I is the identity mapping on H. A is said to satisfy the range condition if cl(D(A)) ⊆ R(I + rA) for each r > 0. For monotone mappings, there are many rel...

In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive nonself-mapping and the set of solutions of the variational inequality for an inversestrongly-monotone mapping in a Hilbert space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a commo...

In this work, it is presented iterative schemes for achieving to common points of the solutions set of the system of generalized mixed equilibrium problems, solutions set of the variational inequality for an inverse-strongly monotone operator, common fixed points set of two infinite sequences of relatively nonexpansive mappings and common zero points set of two finite sequences of maximal monot...

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...

In this paper, we first introduce a monotone mapping and its resolvent in general metric spaces.Then, we give two new iterative methods  by combining the resolvent method with Halpern's iterative method and viscosity approximation method for  finding a fixed point of monotone mappings and a solution of variational inequalities. We prove convergence theorems of the proposed iterations  in ...

In this paper we introduce a viscosity relaxed-extragradient method for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping in a real Hilbert space H . The viscosity relaxed-extragradient method is based on two methods: extragradientlike approximation method and ...

We are concerned with surjectivity of perturbations of maximal monotone operators in non-reflexive Banach spaces. While in a reflexive setting, a classical surjectivity result due to Rockafellar gives a necessary and sufficient condition to maximal monotonicity, in a nonreflexive space we characterize maximality using a “enlarged” version of the duality mapping, introduced previously by Gossez....

For a maximal monotone operator T in a Banach space an iterative solution of 0 ∈ Tx has been found through weak and strong convergence of resolvents of these operators. Identity mapping in the definition of resolvents has been replaced by the duality mapping. Solution after finite steps has also been established.

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...