In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and gen...

This paper introduce a iteration scheme for approximation of strongly accretive operator equations in reflexive Banach space with weakly continuous duality mapping. Our result improve the results of Y. Xu [Ishikawa and Mann Iterative Processes with Errors for Nonlinear Strongly Accretive Operator Equations, J. Math. Anal Appl. 224(1998) 91-101] and I. Inchan and S. Plubtieng [Approximating solu...

Let A be a positive self-adjoint operator and let B be an m-accretive operator which is A-small with a relative bound less than one. Let H = A + B, then H is well-deened on dom(H) = dom(A) and m-accretive. If B is a strictly m-accretive operator obeying dom((H)) dom(A) \ dom((B)) 6 = f0g for some 2 (0; 1]; (1) then for the Trotter product formula we prove that ?

Suppose that X is an arbitrary real Banach space and T : X → X is a Lipschitz continuous φ-strongly accretive operator or uniformly continuous φ-strongly accretive operator. We prove that under different conditions the three-step iteration methods with errors converge strongly to the solution of the equation Tx = f for a given f ∈ X.

We establish some relationships between an m-accretive operator and its Moore-Penorse inverse. derive perturbation result the inverse of a maximal accretive operator. As application we give factorization theorem for quadratic pencil operators. Also, study existence, uniqueness, regularity strict solution complete abstract second order differential equation. Illustrative examples are also given.

In this paper, Φ-pseudo-contractive operators and Φ-accretive operators, more general than the strongly pseudo-contractive operators and strongly accretive operators, are introduced. By setting up a new inequality, authors proved that if → : T X X is a uniformly continuous Φ-pseudo-contractive operator then T has unique fixed point q and the Mann iterative sequence with random errors approximat...

There are various ways to regularize ill-posed operator equations in Hilbert space. If the underlying operator is accretive then Lavrentiev regularization (singular perturbation) is an immediate choice. The corresponding convergence rates for the regularization error depend on the given smoothness assumptions, and for general accretive operators these may be both with respect to the operator or...

We introduce and study a new class of general nonlinear random multivalued operator equations involving generalized m-accretive mappings in Banach spaces. By using the Chang’s lemma and the resolvent operator technique for generalized m-accretive mapping due to Huang and Fang 2001 , we also prove the existence theorems of the solution and convergence theorems of the generalized random iterative...

In this article, we employ certain properties of the transform $\mathscr{C}_{M,m}(A)=(M\mathbf1_{\mathcal{H}}-A^*)(A-m\mathbf1_{\mathcal{H}})$ to obtain new inequalities for bounded linear operator $A$ on a complex Hilbert space $\mathcal{H}$. particular, relations among $|A|,|A^*|,|\mathfrak{R}A|$ and $|\mathfrak{I}A|$. Further numerical radius that extend some known will be presented too.

We give an Itô formula associated to a non-linear semi-group associated to a m-accretive operator.