Bounded Solutions for Fuzzy Integral Equations

We study conditions under which the solutions of a fuzzy integral equation are bounded. 1. Introduction. The concept of set-valued functions and their calculus [2] were found useful in some problems in economics [3], as well as in control theory [17]. Later on, the notion of H-differentiability was introduced by Puri and Ralesku in order to extend the differential of set-valued functions to that of fuzzy functions [29]. This in turn led Seikkala [30] to introduce the notion of fuzzy derivative, which is a generalization of the Hukuhara derivative and the fuzzy integral, which is the same as that proposed by Dubois and Prade [7, 8]. A natural consequence of the above was the study of fuzzy differential and integral equations, Fixed point theorems for fuzzy mappings, an important tool for showing existence and uniqueness of solutions to fuzzy differential and integral equations, have recently been proved by various authors, Lakshmikantham and Vatsala proved the existence of fixed points to fuzzy mappings, using theory of fuzzy differential equations. Finally, stability criteria for the solutions of fuzzy differential systems are given in [21]. In this paper, we examine conditions under which all the solutions of the fuzzy integral equation