Ramy R. Mahmoud

Bio: Ramy R. Mahmoud is an academic researcher from Fayoum University. The author has contributed to research in topics: Fubini's theorem & Algorithm. The author has an hindex of 6, co-authored 16 publications receiving 97 citations. Previous affiliations of Ramy R. Mahmoud include Higher College of Technology.

Weighted Hardy-Type Inequalities on Time Scales with Applications

Abstract: In this paper, we will prove some new dynamic Hardy-type inequalities on time scales with two different weighted functions. The study is to determine conditions on which the generalized inequalities hold using some known hypothesis. The main results will be proved by employing Holder’s inequality, Minkowski’s inequality and a chain rule on time scales. As special cases of our results, when the time scale is the real numbers, we will derive some well-known results due to Copson, Bliss, Flett and Bennett by a suitable choice of the weighted functions. We will apply the results to investigate the oscillation and nonoscillation of a half-linear second order dynamic equation on time scales.

Some new generalized forms of Hardy's type inequality on time scales

Abstract: In this paper, we prove some new dynamic inequalities from which some known dynamic inequalities on time scales, some integral and discrete inequalities due to Hardy, Copson, Chow, Levinson, Pachpatte Yang and Hwang will be deduced as special cases. Also, some new corresponding integral and discrete inequalities will be formulated. The results will be proved by employing the chain rule, integration by parts formula, Hölder’s inequality and Jensen’s inequality on time scales. Mathematics subject classification (2010): 26A15, 26D10, 26D15, 39A13, 34A40, 34N05.

Discrete, Continuous, Delta, Nabla, and Diamond-Alpha Opial Inequalities

Abstract: In this paper, we prove some new diamond-alpha dynamic inequalities of Opial type with one and with two weight functions on time scales. These results contain as special cases improvements of results given in the literature, and these improvements are new even in the important discrete case. Mathematics subject classification (2010): 39A10, 39A12, 26D15.

New generalizations of Németh–Mohapatra type inequalities on time scales

Abstract: Some new dynamic inequalities on time scales are established, that reduce in the discrete and the continuous cases to classical inequalities named after Nemeth and Mohapatra, respectively. The new generalized inequalities resemble intensive classical inequalities known in the literature such as Beesack type inequalities, Copson type inequalities and Hardy–Littlewood type inequalities. The main results will be proved by employing the time scales Holder inequality and the time scales power rules for integrations that have been proved earlier.

A connection between weighted Hardy’s inequality and half-linear dynamic equations

Abstract: In this paper, we give an affirmative answer to the following question: Is the solvability of some nonlinear dynamic equations on a time scale $\mathbb{T}$ not only sufficient but in a certain sense also necessary for the validity of some dynamic Hardy-type inequalities with two different weights? In fact, this answer will give a new characterization of the weights in a weighted Hardy-type inequality on time scales. The results contain the results when $\mathbb{T}=\mathbb{R}$ , $\mathbb{T}=\mathbb{N}$ , and when $\mathbb{T}=q^{\mathbb{N}_{0}}$ as special cases. Some applications are given for illustrations.

On Cauchy–Schwarz inequality for N -tuple diamond-alpha integral

Abstract: In this paper, we present some new Cauchy–Schwarz inequalities for N-tuple diamond-alpha integral on time scales. The obtained results improve and generalize some Cauchy–Schwarz type inequalities given by many authors.

Fractal Calculus of Functions on Cantor Tartan Spaces

Abstract: In this manuscript, integrals and derivatives of functions on Cantor tartan spaces are defined. The generalisation of standard calculus, which is called F η -calculus, is utilised to obtain definitions of the integral and derivative of functions on Cantor tartan spaces of different dimensions. Differential equations involving the new derivatives are solved. Illustrative examples are presented to check the details.

On conformable delta fractional calculus on time scales

Abstract: In this paper, we introduce and investigate the concepts of conformable delta fractional derivative and conformable delta fractional integral on time scales. Basic properties of the theory are proved. c ©2016 All rights reserved.

Some new generalized forms of Hardy's type inequality on time scales

Abstract: In this paper, we prove some new dynamic inequalities from which some known dynamic inequalities on time scales, some integral and discrete inequalities due to Hardy, Copson, Chow, Levinson, Pachpatte Yang and Hwang will be deduced as special cases. Also, some new corresponding integral and discrete inequalities will be formulated. The results will be proved by employing the chain rule, integration by parts formula, Hölder’s inequality and Jensen’s inequality on time scales. Mathematics subject classification (2010): 26A15, 26D10, 26D15, 39A13, 34A40, 34N05.