On Some Problems of Mixed Integral Equations. Analytical discussion of integral equations

      Аннотация: This book presents a solution of the Volterra-Fredholm integralequation (V-FIE) in a Banach space. Under certain conditions, the existence anduniqueness of the solution are proved, using Banach's fixed point theorem. Using a numerical technique the V-FIE leads us to a system of linear Fredholm integral equations (SLFIEs). The normality and the continuity of integral operatorare discussed. The degenerate kernel method (DKM) is used to get the solution of the reduced system.The ideas are interesting and this area caught the attention of many researchers, having so many applications. This paper starts with a brief introduction in the subject and then proposes a new scheme which is discussed in details. The numerical examples illustrate the applicability of the theoretical results.

Ключевые слова: Banach, space, Volterra-Fredholm, integral equation, Degenerate, kernel, Method