Application of fixed point theorem of convex-power operators to nonlinear Volterra type integral equations

摘要

This paper firstly generalizes a kind of new operator, i.e. convex-powercondensing operator, which was obtained by Sun Jingxian in paper [1], anddefines a new class of operator, i.e. P ? convex-power condensing operator inlocally convex space. Also, a new fixed point theorem of this new operator isproved. Finally we apply the results obtained to investigate the existence ofsolutions for nonlinear Volterra type integral equations in locally convexspaces.