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
Kasubai, Gurukul Colony, Ahmedpur, Maharashtra 413 515, India
Received 23 August 2003; Revised 9 May 2004
Copyright © 2004 B. C. Dhage. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.