ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF DIFFERENCE EQUATIONS IN BANACH SPACES.

In this paper we consider the first order difference equation in a Banach space (Multiple line equation(s) cannot be represented in ASCII text). We show that this equation has a solution asymptotically equal to a. As an application of our result we study the difference equation (Multiple line equation(s) cannot be represented in ASCII text) and give conditions when this equation has solutions. In this note we extend the results from [8, 9]. For example, in [9] the function f is a real Lipschitz function. We suppose that f has values in a Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness. [ABSTRACT FROM AUTHOR]