EXISTENCE OF SOLUTION OF NONLINEAR VOLTERRA-HAMMERSTEIN-FREDHOLM INTEGRAL EQUATION IN BANACH ALGEBRA
K. SAKURE *
Department of Mathematics, Govt. Digvijay Auto. P.G. College, Rajnandgaon 491441, India.
*Author to whom correspondence should be addressed.
The aim of the paper is to prove the existence of solution of nonlinear Volterra-Hammerstein- Fredholm integral equation(VHFIE) under certain conditions. The main tools are Darbo’s fixed point theorem and measure of noncompactness for investigating the existence of solution of nonlinear VHFIE. An illustrative example and application of VHFIEs are also given in this paper.
Keywords: Nonlinear integral equation, measure of noncompactness, darbo’s fixed point theorem, existence theorem