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

B. C. Dhage

International Journal of Stochastic Analysis, 2004, vol. 2004, 1-12

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 ) + ∫ 0 σ ( t ) v ( t , s ) g ( s , x ( η ( s ) ) ) d s ) 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.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:129603

DOI: 10.1155/S1048953304308038

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