In this paper, we propose and study several strongly convergent versions of the forward–reflected–backward splitting method Malitsky Tam for finding a zero sum two monotone operators in real Hilbert space. Our proposed methods only require one forward evaluation single-valued operator backward set-valued at each iteration; feature that is absent many other available literature. We also develop ...

with respect to the Euclidian norm, where F :Rn →Rn is a nonlinear operator. Section 2 is devoted to a brief description of asynchronous parallel algorithm. In Section 3, we prove the main result concerning the convergence of the general algorithm in the synchronous case to a fixed point of a nonlinear operator fromRn to Rn. A particular case of this algorithm (algorithm of Jacobi) is applied i...

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 Identity mapping in the definition of resolvents has been replaced by the duality mapping.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.

In this paper, we prove a strong convergence theorem for fixed points of sequence for multivalued nonexpansive mappings and a zero of maximal monotone operator in Banach spaces by using the hybrid projection method. Our results modify and improve the recent results in the literatures.

The aim of this paper is to establish strong convergence theorems for a strongly relatively nonexpansive sequence in a smooth and uniformly convex Banach space. Then we employ our results to approximate solutions of the zero point problem for a maximal monotone operator and the fixed point problem for a relatively nonexpansive mapping.

We give an answer to an open problem regarding the full enlargeability of a maximal monotone operator S : X ⇒ X∗ by Sse, the smallest enlargement belonging to a certain class of enlargements associated to S. Moreover, we prove the weak∗ closedness of the set ShS (ε1, x)+ThT (ε2, x) under a weak generalized interior regularity condition.

Using the properties of almost nonexpansive curves introduced by B. Djafari Rouhani, we study the asymptotic behavior of solutions of nonlinear functional differential equation du(t)/dt + Au(t)+ G(u)(t) f(t), where A is a maximal monotone operator in a nilbert space H,f E LI(0,:H) and G:C([O,c):D(A))LI(O,c:H)is a given mapping.