Abstract
AbstractIn this paper, we present new fixed point theorems in Banach algebras relative to the weak topology. Our fixed point results are obtained under Leray-Schauder-type boundary conditions. These results improve and complement a number of earlier works. As an application, we establish some existence results for a broad class of quadratic integral equations.
Highlights
The need for a fixed point theory in Banach algebras arose out of the study of quadratic integral equations
The problem of existence of solution to quadratic integral equations may be usually reduced to a fixed point problem of the form
Significant advances have been made in the development of fixed point theory in Banach algebras using the norm topology and applications to quadratic integral equations
Summary
The need for a fixed point theory in Banach algebras arose out of the study of quadratic integral equations. The aim of this paper is to establish new fixed point theorems in Banach algebras relative to the weak topology under Leray-Schauder-type boundary conditions. We prove some fixed point theorems in Banach algebras relative to the weak topology. Let M be a nonempty bounded subset of a Banach algebra X, and A, C : X → X be Lipschitzian mappings with constants αA and αC such that M αA + αC
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