In this paper, we introduce a new resolvent operator and we call it relaxed resolvent operator. We prove that relaxed resolvent operator is single-valued and Lipschitz continuous and finally we approximate the solution of a variational inclusion problem in Hilbert spaces by defining an iterative algorithm based on relaxed resolvent operator. A few concepts like Lipschitz continuity and strong m...

We show that every free semigroup algebras has a (strongly) unique Banach space predual. We also provide a new simpler proof that a weak-∗ closed unital operator operator algebra containing a weak-∗ dense subalgebra of compact operators has a unique Banach space predual.

Let A and B be bounded linear operators on a Banach space such that ABA = A2 and BAB = B2. Then A and B have some spectral properties in common. This situation is studied in the present paper. 1. Terminology and motivation Throughout this paper X denotes a complex Banach space and L(X) the Banach algebra of all bounded linear operators on X. For A ∈ L(X), let N(A) denote the null space of A, an...

By introducing the concepts of order almost Dunford-Pettis and almost weakly limited operators in Banach lattices, we give some properties of them related to some well known classes of operators, such as, order weakly compact, order Dunford-Pettis, weak and almost Dunford- Pettis and weakly limited operators. Then, we characterize Banach lat- tices E and F on which each operator from E into F t...

This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving (A, η)-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used to study the (A, η)-monotonicity. Using the generalized resolvent operator technique and the semi-inner product structure, the approximation solvability of the proposed problem is inve...

Using the notion of a Banach operator, we have obtained a decompositional property of a Hilbert space, and the equality of two invertible bounded linear multiplicative operators on a normed algebra with identity. 1. Introduction. This paper is a continuation of our earlier work [7] on Banach operators. We recall that if X is a normed space and α : X → X is a mapping, then following [4], α is sa...

Modifying von Neumann’s alternating projections algorithm, we obtain an alternating method for solving the recently introduced Common Solutions to Variational Inequalities Problem (CSVIP). For simplicity, we mainly con…ne our attention to the two-set CSVIP, which entails …nding common solutions to two unrelated variational inequalities in Hilbert space. Keywords: Alternating method, averaged op...

The main purpose of this paper is to introduce and study a new class of generalized nonlinear setvalued quasi-variational inclusions system involving A, η -accretive mappings in Banach spaces. By using the resolvent operator due to Lan-Cho-Verma associated with A, η -accretive mappings and the matrix analysis method, we prove the convergence of a new hybrid proximal point three-step iterative a...