This paper is dedicated to study a new class of general nonlinear random A-maximal m-relaxed η-accretive (so called (A, η)-accretive [49]) equations with random relaxed cocoercive mappings and random fuzzy mappings in q-uniformly smooth Banach spaces. By utilizing the resolvent operator technique for A-maximal m-relaxed η-accretive mappings due to Lan et al. and Chang’s lemma [13], some new ite...

There are two important connections between the classes of nonexpansive and of accretive mappings which give rise to a strong connection between the fixed point theory of nonexpansive mappings and the mapping theory of accretive maps. These are: (1) If U is a nonexpansive mapping of D(U) into X, and if we set T — I--U, D(T)=D(U), then T is an accretive mapping of D{T) into X. (2) If { U(i)f t^O...

In the sequel, we shall denote the single-valued normalized duality map by j. Let F (T ) = {x ∈ E : Tx = x} denote the set of all fixed point for a mapping T . We write xn ⇀ x (respectively xn ∗ ⇀ x) to indicate that the sequence xn weakly (respectively weak∗) converges to x; as usual xn → x will symbolize strong convergence. A mapping A : D(A) ⊂ E → 2 is called to be accretive if for all x, y ...

in this paper, we use the concept of graph convergence of h(.,.)-co-accretive mapping introduced by [r. ahmad, m. akram, m. dilshad, graph convergence for the h(.,.)-co-accretive mapping with an application, bull. malays. math. sci. soc., doi: 10.1007/s40840-014-0103-z, 2014$] and define an over-relaxed proximal point method to obtain the solution of a generalized variational inclusion problem ...

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 work, we present a bilinear Tb theorem for singular integral operators of Calderón-Zygmund type. We prove some new accretive type Littlewood-Paley results and construct a bilinear paraproduct for a para-accretive function setting. As an application of our bilinear Tb theorem, we prove product Lebesgue space bounds for bilinear Riesz transforms defined on Lipschitz curves.

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 study a new system of nonlinear set-valued variational inclusions involving a finite family of H ·, · -accretive operators in Banach spaces. By using the resolvent operator technique associated with a finite family of H ·, · -accretive operators, we prove the existence of the solution for the system of nonlinear set-valued variational inclusions. Moreover, we introduce a new iterative scheme...

A new class of generalized nonlinear set-valued quasivariational inclusions involving generalizedm-accretive mappings in Banach spaces are studied, which included many variational inclusions studied by others in recent years. By using the properties of the resolvent operator associated with generalized m-accretive mappings, we established the equivalence between the generalized nonlinear set-va...

We introduce a class of η-accretive mappings in a real Banach space and show that the η-proximal point mapping for η-m-accretive mapping is Lipschitz continuous. Further, we develop an iterative algorithm for a class of general variational-like inclusions involving ηaccretive mappings in real Banach space, and discuss its convergence criteria. The class of η-accretivemappings includes several i...