On some nonlinear alternatives of Leray-Schauder type and functional integral equations

B. C. Dhage

Kasubai, Gurukul Colony, Ahmedpur-413 515, Dist Latur, Maharashtra, India

E-mail. bcd20012001@yahoo.co.in

In this paper, some new fixed point theorems concerning the nonlinear alternative of Leray-Schauder type are proved in a Banach algebra. Applications are given to nonlinear functional integral equations in Banach algebras for proving the existence results. Our results of this paper complement the results that appear in Granas et. al. \cite{GGL} and Dhage and Regan \cite{DR}.

AMSclassification. 47H10.

Keywords. Banach algebra, fixed point theorem, integral equations.