Journal of Applied Mathematics and Stochastic Analysis 
Volume 2004 (2004), Issue 3, Pages 271-282
doi:10.1155/S1048953304308038

On existence of extremal solutions of nonlinear functional integral equations in Banach algebras

B. C. Dhage

 Kasubai, Gurukul Colony, Ahmedpur, Maharashtra 413 515, India
Received 23 August 2003; Revised 9 May 2004

Abstract

An algebraic fixed point theorem involving the three operators in a Banach algebra is proved using the properties of cones and they are further applied to a certain nonlinear integral equations of mixed type x(t)=k(t,x(μ(t)))+[f(t,x(θ(t)))](q(t)+∫0σ(t)v(t,s)g(s,x(η(s)))ds) for proving the existence of maximal and minimal solutions. Our results include the earlier fixed point theorems of Dhage (1992 and 1999) as special cases with a different but simple method.