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...

K e y w o r d s H a c c r e t i v e operator, Resolvent operator technique, Variational inclusion, Iterative algorithm. 1. I N T R O D U C T I O N A N D P R E L I M I N A R I E S Variational inequalities and variational inclusions are among the most interesting and important mathematical problems and have been studied intensively in the past years since they have wide applications in mechanics,...

Let X be a real Banach space, J = [0, a] ⊂ IR, A : D(A) ⊂ X → 2 \ ∅ an m-accretive operator and f : J × X → X continuous. In this paper we obtain necessary and sufficient conditions for weak positive invariance (also called viability) of closed sets K ⊂ X for the evolution system u′ +Au f(t, u) on J = [0, a]. More generally, we provide conditions under which this evolution system has mild solut...

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...

In the setting of hyperbolic spaces, we show that convergence Browder-type sequences and Halpern iterations respectively entail their viscosity version with a Rakotch map. We also hybrid Krasnoselskii-Mann iteration follows from Browder type sequence. Our results follow proof-theoretic techniques (proof mining). From an analysis theorems due to T. Suzuki, extract transformation rates for origin...

In this paper the continuity of the solutions of a mathematical model of thermoviscoelasticity with respect to the model parameters is proved. This was an open problem conjectured iIi [27J and [28]. The nonlinear partial differential equations under consideration arise from the conservation laws of linear momentum and energy and describe structural phase transitions in solids with non-convex La...

A two-phase two-component model is formulated for the advective-diffusive transport of methane in liquid phase through sediment with the accompanying formation and dissolution of methane hydrate. This free-boundary problem has a unique generalized solution in L; the proof combines analysis of the stationary semilinear elliptic Dirichlet problem with the nonlinear semigroup theory in Banach spac...

‎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.