Let X and Y be real Banach spaces, ƒ a mapping of X into 2, y0 an element of Y It is our object in the present discussion to present a new existence theory for solutions of the equation y0£f(x) which extends, sharpens, and simplifies the corresponding theory for X — Y and ƒ hypermaximal accretive. This new existence theory is founded in a very basic way upon the fixed point theory of self-mappi...

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

This work aims to develop a new class of accretive mappings and investigate its associated proximal mappings. is known as generalized (Hk,φ)-η-accretive Further, the research includes discussion application, leading set-valued variational-like inclusions (SVVLI, in short) semi-inner product spaces. The corresponding fixed point problem for SVVLI given. used provide an iterative scheme solving S...

We will extend the definition of antieigenvalue of an operator to antieigenvalue-type quantities, in the first section of this paper, in such a way that the relations between antieigenvalue-type quantities and their corresponding Kantorovich-type inequalities are analogous to those of antieigenvalue and Kantorovich inequality. In the second section, we approximate several antieigenvaluetype qua...

A general nonlinear framework for an Ishikawa-hybrid proximal point algorithm using the notion of A, η -accretive is developed. Convergence analysis for the algorithm of solving a nonlinear set-valued inclusions problem and existence analysis of solution for the nonlinear set-valued inclusions problem are explored along with some results on the resolvent operator corresponding to A, η -accretiv...

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...

The operator B in a complex Hubert space H is said to form an angle Θ with the (stronger) operator A if D(A) c D(B) and, for every x in D(A), (Ax, Bx)π belongs to the cone K(θ) of all complex z with | arg (z) \ ̂ θ. If A and I? are closed maximal accretive operators and B forms a right angle with A, then A + JE> is closed maximal accretive and the Cauchy problem for each of the equations u(t) -f...

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...

‎The purpose of this paper is to introduce a new mapping for a finite‎ ‎family of accretive operators and introduce an iterative algorithm‎ ‎for finding a common zero of a finite family of accretive operators‎ ‎in a real reflexive strictly convex Banach space which has a‎ ‎uniformly G^ateaux differentiable norm and admits the duality‎ ‎mapping $j_{varphi}$‎, ‎where $varphi$ is a gauge function ...

In this paper, we introduce and study a new iterative algorithm for approximating zeroes of accretive operators in Banach spaces.