Mathematics and Computer Applications - Sciene

Planar noninvertible maps have been studied recently by several authors such as Mira , Gardini , Cathala.

The main theme of this thesis is oriented toward three objectives.The first objective, is a study to fuzzy set theory with some basic properties related to differential equations.The second objective, is a study and prove of the existence and uniqueness theorem of fuzzy differential equations using two approaches, the first is by Brower fixed point theorem and the other by Schauder fixed point theorem.

Let H(U) be the set of all holomorphic functions on the unit ball U of the complex plane. The Hardy space H² is the set of all functions f(z)= that belongs to H(U) such that  < ¥. Let j be a holomorphic self map of U. The composition operator C_j on H² is defined as follows:

C_jf = foj, for all f Î H²