Existence of solutions of system of functional-integral equations using measure of noncompactness

Document Type : Research Paper


1 Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore-632014, TN, INDIA

2 Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran

3 Department of Mathematics‎, ‎Texas A \& M University‎ - ‎Kingsville‎ - ‎78363-8202‎, ‎Texas‎, ‎USA‎‎


‎We propose to investigate the solutions of system of functional-integral‎ ‎equations in the setting of measure of noncompactness on real-valued bounded and continuous Banach space‎. To achieve this‎, ‎we first establish some new Darbo type fixed and coupled fixed point results for‎ $\mu$-set $(\omega,\vartheta)$-contraction operator‎ ‎using arbitrary measure of noncompactness in Banach spaces‎. An example is given in support for the solutions of a pair of system of functional-integral‎ equations‎.