On a fixed point theorem in Banach algebras with applications

In this article it is shown that some of the hypotheses of a fixed point theorem of the present author [B.C. Dhage, On some variants of Schauder's fixed point principle and applications to nonlinear integral equations, J. Math. Phys. Sci. 25 (1988) 603-611] involving two operators in a Banach algebra are redundant. Our claim is also illustrated with the applications to some nonlinear functional integral equations for proving the existence results.