Abstract
We study Frechet differentiable stable operators in real Banach spaces. We present the theory of linear and nonlinear stable operators in a systematic way and prove solvability theorems for operator equations with differentiable expanding operators. In addition, some relations to the theory of monotone operators in Hilbert spaces are discussed. Using the obtained solvability results, we formulate the corresponding fixed point theorem for a class of nonlinear expanding operators.
Highlights
IntroductionWhere A : X → X is a nonlinear operator
The basic inspiration for studying stable and strongly stable operators in a real Banach space X is the operator equation of the form A(x) = a, a ∈ X, (1.1)where A : X → X is a nonlinear operator
The aim of this paper is to study a class of Frechet differentiable stable operators and to prove a solvability theorem for nonlinear operator equations (1.1) with differentiable expanding operators
Summary
Where A : X → X is a nonlinear operator. We consider a single-valued mapping A, whose domain of definition is X and whose range R(A) is contained in X. Throughout this paper, the terms mapping, function, and operator will be used synonymously. We start by recalling some basic concepts and preliminary results (see, e.g., [29]). Where g : R+ → R+ is a strictly monotone increasing and continuous function with g(0) = 0, lim g(t) = +∞. The function g(·) is called a stabilizing function of the operator A.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
