VOLTERRA AND FREDHOLM INTEGRAL EQUATIONS IN LOCALLY CONVEX SPACES, AND LEADER-TYPE CONTRACTIONS IN GAUGE SPACES

Abstract

There are the several different methods concerning studies of quadratic, quadratic fractional, linear and nonlinear integral equations of Volterra- and Fredholm-type in various spaces. Method of studies of such equations in locally convex spaces with approximation procedure and presented here is new, general, optimal and precise, and also different from those known in the literature. Examples provided in this paper illustrate chosen aspects of our method. The main tools used here are based on our special cases of very general and stronger periodic point, fixed point and approximation theorems concerning not necessarily continuous dynamic systems in not necessarily sequentially complete or separable gauge spaces.