Prologue

Abstract

To quote S.M. Ulam (1960) (page 63)¹ for very general functional equations, one can ask the following question. When is it true that the solution of an equation differing slightly from a given one, must of necessity be close to the solution of the given equation? Similarly, if we replace a given functional equation by a functional inequality, when can one assert that the solutions of the inequality lie near the solutions of the strict equation? The present work is designed to provide an introduction to the formulation and solution of such problems by examination of various researches most of which has been carried out during the last two decades.