Abstract
AbstractIn this paper, we provide a new approach for discussing the solvability of a class of operator equations by establishing fixed point theorems in locally convex spaces. Our results are obtained extend some Krasnosel’skii type fixed point theorems. As an application, we investigate the existence and global attractivity of solutions for a general nonlinear integral equation of mixed type of Urysohn and Volterra.
Highlights
As an example of algebraic settings, the captivating Krasnosel’skii’s fixed point theorem leads to the consideration of fixed points for the sum of two operators
If M is a bounded, closed, and convex subset of a Banach space X and A, B are two mappings from M into X such that A is compact and B is a contraction, A(M) + B(M) ⊆ M, A + B has at least one fixed point in M
In Section, we prove the existence and the global attractivity of solutions for equation ( . )
Summary
As an example of algebraic settings, the captivating Krasnosel’skii’s fixed point theorem (see [ ] or [ ], p. ) leads to the consideration of fixed points for the sum of two operators. Suppose that M is a closed and convex subset of X, and the operators A : M → Y and F : X × Y → X satisfy the following conditions: (i) A is continuous, and A(M) is a relatively compact subset of Y ; (ii) F is continuous, and for each ρ ∈ there exists αρ ∈ [ , ) such that
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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
