Samir Saker | Mansoura University (original) (raw)

Papers by Samir Saker

Journal of Mathematics and Computer Science, 2020

Applied Mathematics & Information Sciences, 2015

In this paper, we prove some new integral inequalities of Hardy's type on time scales. The Ha... more In this paper, we prove some new integral inequalities of Hardy's type on time scales. The Hardy inequalities have many applications especially in proving the boundedness Cesaro operators. The main results will be proved by making use of some algebraic inequalities, the Holder inequality and a simple consequence of Keller's chain rule on time scales. The discrete inequ alities that we will derive from our results in the discrete time scales are essen tially new.

Proceedings of the American Mathematical Society, 2020

The main objective of this paper is a study of the structure and basic properties of the weighted... more The main objective of this paper is a study of the structure and basic properties of the weighted discrete Gehring classes, as well as the study of the relationship between discrete Muckenhoupt and Gehring classes. First, we prove that the weighted discrete Muckenhoupt class A λ 1 ( C ) \mathcal {A}_{\lambda }^{1}(C) , C > 1 C>1 , consisting of nonincreasing sequences, belongs to the weighted discrete Gehring class G λ p ( A ) \mathcal {G}_{\lambda }^{p}(A) by giving explicit values of exponent p p and constant A A . Next, we prove the self-improving property of the weighted Gehring class G λ p ( K ) \mathcal {G}_{\lambda }^{p}({K)} , p > 1 p>1 , K > 1 K>1 , consisting of nonincreasing sequences. The exponent and constant of transition are explicitly given. Finally, utilizing the self-improving property of the weighted Gehring class, we also derive the self-improving property of a discrete Muckenhoupt class A p ( C ) \mathcal {A}^{p}(C) , p > 1 p>1 , C > 1...

Proceedings of the Edinburgh Mathematical Society, 2019

In this paper, we prove some reverse discrete inequalities with weights of Muckenhoupt and Gehrin... more In this paper, we prove some reverse discrete inequalities with weights of Muckenhoupt and Gehring types and use them to prove some higher summability theorems on a higher weighted space lwp(openN)l_{w}^{p}({\open N})lwp(openN) form summability on the weighted space lwq(openN)l_{w}^{q}({\open N})lwq(openN) when p>q. The proofs are obtained by employing new discrete weighted Hardy's type inequalities and their converses for non-increasing sequences, which, for completeness, we prove in our special setting. To the best of the authors' knowledge, these higher summability results have not been considered before. Some numerical results will be given for illustration.

Applicable Analysis and Discrete Mathematics, 2017

In this paper, we will prove some new dynamic inequalities of Hilbert's type on time scales. ... more In this paper, we will prove some new dynamic inequalities of Hilbert's type on time scales. Our results as special cases extend some obtained dynamic inequalities on time scales.and also contain some integral and discrete in- equalities as special cases. We prove our main results by using some algebraic inequalities, H?older's inequality, Jensen's inequality and a simple consequence of Keller's chain rule on time scales.

Axioms

In this paper, we develop a new technique on a time scale T to prove that the self-improving prop... more In this paper, we develop a new technique on a time scale T to prove that the self-improving properties of the Muckenhoupt weights hold. The results contain the properties of the weights when T=R and when T=N, and also can be extended to cover different spaces such as T=hN, T=qN, etc. The results will be proved by employing some new refinements of Hardy’s type dynamic inequalities with negative powers proven and designed for this purpose. The results give the exact value of the limit exponent as well as the new constants of the new classes.

Bulletin of the Australian Mathematical Society, 2017

In this paper, we prove some new reverse dynamic inequalities of Renaud- and Bennett-type on time... more In this paper, we prove some new reverse dynamic inequalities of Renaud- and Bennett-type on time scales. The results are established using the time scales Fubini theorem, the reverse Hölder inequality and a time scales chain rule.

Journal of Mathematics and Computer Science

Frontiers in Functional Equations and Analytic Inequalities, 2019

In this chapter, we establish some inequalities of Hardy and Leindler type and their converses vi... more In this chapter, we establish some inequalities of Hardy and Leindler type and their converses via conformable calculus with weighted functions. As applications, we obtain some classical integral inequalities as special cases.

In this paper, the authors consider the second-order neutral functional differential equation [p(... more In this paper, the authors consider the second-order neutral functional differential equation [p(t)ψ(y(t))(x(t)) ]′ + q(t)f(y(δ(t))) = 0, t ≥ t0, where x(t) = y(t) + r(t)y(τ(t)) and γ > 0 is a ratio of odd positive integers. They establish some new sufficient conditions for oscillation of all solutions that are substantial improvements to some existing results in the literature. Some examples are included to illustrate the main results. AMS (MOS) Subject Classification. 34K11, 34K40

gmj, 2003

Using the Riccati transformation techniques, we establish some new oscillation criteria for the s... more Using the Riccati transformation techniques, we establish some new oscillation criteria for the second-order nonlinear difference equation Some comparison between our theorems and the previously known results in special cases are indicated. Some examples are given to illustrate the relevance of our results.

Demonstratio Mathematica, 2002

Annales Polonici Mathematici, 2021