A certain integral-recurrence equation with discrete-continuous auto-convolution

Mircea I. Cîrnu

Address: Department of Mathematics III, Faculty of Applied Sciences, Universtity Politehnica of Bucharest, Romania

E-mail: cirnumircea@yahoo.com

Abstract: Laplace transform and some of the author’s previous results about first order differential-recurrence equations with discrete auto-convolution are used to solve a new type of non-linear quadratic integral equation. This paper continues the author’s work from other articles in which are considered and solved new types of algebraic-differential or integral equations.

AMSclassification: primary 45G10; secondary 44A10.

Keywords: integral-recurrence equation, first order differential recurrence equations, discrete-continuous convolution, combinatorial discrete-continuous convolution, auto-convolution, Laplace transform.