On [p,q]-Order of Growth and Fixed Points of Solutions and Their Arbitrary-order Derivatives of Linear Differential Equations in the Unit Disc

Abstract

Overall, the subject of this thesis was devoted to the growth and xed points of solutions of linear differential equations of the form (k) (k 1) 0 A (z) f + A (z) f + + A (z) f + A (z) f = 0; 1 0 k k 1 in the case where A (z) 6 0 (i = 0; 1; :::; k and k > 2) are analytic functions in the unit disc by i using the concept of [p; q]-order. During this work, we mentioned some results, in which we studied the [p; q]-order and the [p; q]-exponent of convergence of the sequence of distinct xed points of solutions and their ar- bitrary order derivatives of general high-order linear di⁄erential equations cited above, and this leads us to ask the following questions: Is it possible to obtain similar results for a sector of the unit disc? And can we generalize the results when the coefficients are meromorphic functions and for non-homogeneous linear differential equations? And under what conditions would this generalization be possible?