Marian Kwapisz

Some existence and uniqueness results for boundary value problems for difference equations

Existence and uniqueness results for bvp problems for difference equations are discussed. The weighted norm technique and the Banach contraction mapping principle are employed

ON DISCRETE EQUATIONS, INEQUALITIES AND INTERVAL EVALUATIONS OF FIXED POINTS OF ISOTONE - ANTITONE MAPPINGS

Publisher Summary This chapter describes the discrete equations, inequalities, and interval evaluations of fixed points of isotone–antitone mappings. It presents the general form of discrete Volterra equations and inequalities. Under suitable assumptions, a result on discrete inequalities is established. The result permits in receiving an interval evaluation for solutions to discrete equations with isotone–antitone operators. Results for recurrent equations and inequalities can be derived as a special case of the result mentioned. The chapter discusses the interval evaluations of fixed points of a class of operators. It presents a theorem that states that there exists a unique solution of the Volterra discrete problem. An important special case of the Volterra discrete equation is recurrent equations.

GENERAL INEQUALITIES AND FIXED-POINT PROBLEMS

The aim of the present paper is to give some general results on fixed-point problems in the setting of an abstract set equipped only with a rather simple mathematical structure.