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

B. C. Dhage
2004 Journal of Applied Mathematics and Stochastic Analysis  
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 typex(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.
doi:10.1155/s1048953304308038 fatcat:cpawygwgdbedvhtxlrqkb7c2n4