Abstract
AbstractThe aim of this paper is to establish some new fixed point theorems for the superposition operators in locally convex spaces which satisfy the Krein-S̆mulian property. We employ a family of measures of noncompactness in conjunction with the Schauder-Tychonoff fixed point theorem. As an application, the existence of solutions to a quite general nonlinear Volterra type integral equation is considered in locally integrable spaces.
Highlights
As an example of algebraic settings, the captivating Krasnosel’skii fixed point theorem leads to the consideration of fixed points for the sum of two operators
If M is a nonempty, bounded, closed, and convex subset of a Banach space X and A, B are two maps from M into X such that A(M) + B(M) ⊆ M, A is compact and B is a contraction, A + B has at least one fixed point in M
Several papers have given generalizations of this theorem involving the weak topology of Banach spaces by using the De Blasi measure of weak noncompactness
Summary
As an example of algebraic settings, the captivating Krasnosel’skii fixed point theorem leads to the consideration of fixed points for the sum of two operators.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
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 call