On [p,q]-order Of Growth And Fixed Points Of Solutions And Their Arbitrary-order Derivatives Of Linear Differential Equations In The Unit Disc

Résumé: 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?

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