Papers by Mahmoud M . Osman
Annales Polonici Mathematici
In this paper, we prove some new characterizations of the weighted functions such that norm dynam... more In this paper, we prove some new characterizations of the weighted functions such that norm dynamic inequalities of mixed type involving operators of Hardy's type with general kernels, of the form , hold for 1 < p ≤ q < ∞ and 1 < q < p < ∞, where HKf (x) := σ(x) a K(σ(x), y)f (y) ∆y (here u and υ are the weight functions). Corresponding results are also obtained for the adjoint operator H * K f (x) := ∞ x K(x, σ(y))f (y) ∆y, where σ(x) is the forward jump operator on time scales. Our results include some well known inequalities in the literature.
Two Weighted Norm Dynamic Inequalities with Applications on Second Order Half-Linear Dynamic Equations
Qualitative Theory of Dynamical Systems
Dynamic Systems and Applications, 2017
ABSTRACT. In this paper, we present some new generalizations of dynamic Opial-type inequalities o... more ABSTRACT. In this paper, we present some new generalizations of dynamic Opial-type inequalities of higher order on time scales. The results contain as special cases many of the results currently given in literature. As an application, we apply these inequalities together with a Hardy-type inequality on time scales to establish some lower bounds of the distance between zeros of a solution and/or its derivatives for a fourth-order dynamic equation. AMS (MOS) Subject Classification. 34A40, 34N05, 39A10, 39A13, 26D10, 26D15.
Inequalities of Hardy type and generalizations on time scales
Analysis
In this paper, we prove some new dynamic inequalities on time scales which as special cases conta... more In this paper, we prove some new dynamic inequalities on time scales which as special cases contain several generalizations of integral and discrete inequalities due to Hardy, Copson, Leindler, Bennett, Pachpatte and Pečarić and Hanjš.
In this paper we prove some new dynamic inequalities with two weight functions and some new dynam... more In this paper we prove some new dynamic inequalities with two weight functions and some new dynamic inequalities with two unknown functions of Opial type on time scales. The main results will be proved by employing Hölder's inequality, the chain rule and some basic algebraic inequalities.
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Papers by Mahmoud M . Osman