Samir H. Saker
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View article: Unified Framework for Continuous and Discrete Relations of Gehring and Muckenhoupt Weights on Time Scales
Unified Framework for Continuous and Discrete Relations of Gehring and Muckenhoupt Weights on Time Scales Open
This article contains some relations, which include some embedding and transition properties, between the Muckenhoupt classes Mγ;γ>1 and the Gehring classes Gδ;δ>1 of bi-Sobolev weights on a time scale T. In addition, we establish the rela…
View article: Fundamental Properties of Muckenhoupt and Gehring Weights on Time Scales
Fundamental Properties of Muckenhoupt and Gehring Weights on Time Scales Open
Some fundamental properties of the Muckenhoupt class Ap of weights and the Gehring class Gq of weights on time scales and some relations between them will be proved in this paper. To prove the main results, we will apply an approach based …
View article: Some Hardy's inequalities on conformable fractional calculus
Some Hardy's inequalities on conformable fractional calculus Open
In this article, we will demonstrate some Hardy’s inequalities by utilizing Hölder inequality, integration by parts, and chain rule of the conformable fractional calculus. When α = 1 \alpha =1 , we can obtain some of classical Copson’s a…
View article: Discrete Rubio De Francia extrapolation theorems in the theory of Bp−discrete weights
Discrete Rubio De Francia extrapolation theorems in the theory of Bp−discrete weights Open
In this paper, we will prove some discrete Rubio De Francia extrapolation theorems for nonincreasing sequences in the setting of the discrete Bp-weights. We also present some extensions to the discrete B?-weights. The proof of the results …
View article: Self-Improving Properties of Continuous and Discrete Muckenhoupt Weights: A Unified Approach
Self-Improving Properties of Continuous and Discrete Muckenhoupt Weights: A Unified Approach Open
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 c…
View article: On Discrete Weighted Lorentz Spaces and Equivalent Relations between Discrete ℓp-Classes
On Discrete Weighted Lorentz Spaces and Equivalent Relations between Discrete ℓp-Classes Open
In this paper, we study some relations between different weights in the classes Bp,Bp*,Mp and Mp* that characterize the boundedness of the Hardy operator and the adjoint Hardy operator. We also prove that these classes generate the same we…
View article: Exact exponents for inclusion of discrete Muckenhoupt classes into Gehring classes and reverse
Exact exponents for inclusion of discrete Muckenhoupt classes into Gehring classes and reverse Open
In this paper, we establish some embedding relationships between Muckenhoupt and Gehring classes A p and G r by proving transition and inclusion relations.We also identify the exact range of τ > 1 for which w τ ∈ A p .Additionally, we show…
View article: Mathematical Analysis of an SIVRWS Model for Pertussis with Waning and Naturally Boosted Immunity
Mathematical Analysis of an SIVRWS Model for Pertussis with Waning and Naturally Boosted Immunity Open
This work aims mainly to study the controllability of pertussis infection in the presence of waning and natural booster of pertussis immunity and to study their impact on the overall dynamics and disease outcomes. Therefore, an SIVRWS (Sus…
View article: Some further properties of discrete Muckenhoupt and Gehring weights
Some further properties of discrete Muckenhoupt and Gehring weights Open
The main objective of this paper is a further study of discrete Muckenhoupt and Gehring weights.We first restate monotonicity properties of Muckenhoupt and Gehring classes in terms of the corresponding norms.In addition, we establish some …
View article: Ostrowski type integral inequalities, weighted Ostrowski, and trapezoid type integral inequalities with powers
Ostrowski type integral inequalities, weighted Ostrowski, and trapezoid type integral inequalities with powers Open
In this paper, we prove some new weighted Ostrowski and Trapezoid type inequalities with powers on time scales.The results will be proved by employing the generalized version of Montgomery identity with weights on time scales designed and …
View article: Asymptotic properties of solutions of third-order nonlinear dynamic equations on time scales
Asymptotic properties of solutions of third-order nonlinear dynamic equations on time scales Open
This paper is concerned with the asymptotic properties of solutions of third-order nonlinear dynamic equations on time scales.Some sufficient conditions for oscillation and nonoscillation of solutions as well as the boundedness of the solu…
View article: On discrete weighted Hardy type inequalities and properties of weighted discrete Muckenhoupt classes
On discrete weighted Hardy type inequalities and properties of weighted discrete Muckenhoupt classes Open
In this paper, first we prove some new refinements of discrete weighted inequalities with negative powers on finite intervals. Next, by employing these inequalities, we prove that the self-improving property ( backward propagation property…
View article: Self-improving properties of weighted Gehring classes with applications to partial differential equations
Self-improving properties of weighted Gehring classes with applications to partial differential equations Open
In this paper, we prove that the self-improving property of the weighted Gehring class $G_{\lambda }^{p}$ with a weight λ holds in the non-homogeneous spaces. The results give sharp bounds of exponents and will be used to obtain the s…
View article: Some new Opial type dynamic inequalities via convex functions and applications
Some new Opial type dynamic inequalities via convex functions and applications Open
In this paper, we prove some new Opial-type dynamic inequalities on time scales. Our results are obtained in frame of convexity property and by using the chain rule and Jensen and Hölder inequalities. For illustration purpose, we obtain so…
View article: Characterizations of weighted dynamic Hardy-type inequalities with higher-order derivatives
Characterizations of weighted dynamic Hardy-type inequalities with higher-order derivatives Open
In this paper, we establish some necessary and sufficient conditions for the validity of a generalized dynamic Hardy-type inequality with higher-order derivatives with two different weighted functions on time scales. The corresponding cont…
View article: Weighted Gehring and Muckenhoupt classes and some inclusion properties with norm inequalities
Weighted Gehring and Muckenhoupt classes and some inclusion properties with norm inequalities Open
In this paper, we will prove some fundamental properties of the power mean operator H λ w p of order p, which is defined bywhere λ and w are nonnegative functions and Λ (x) = x 0 λ (s) ds.Then by using these properties we will establish so…
View article: Theory of discrete Muckenhoupt weights and discrete Rubio de Francia extrapolation theorems
Theory of discrete Muckenhoupt weights and discrete Rubio de Francia extrapolation theorems Open
In this paper, we will prove a discrete Rubio De Francia extrapolation theorem in the theory of discrete Ap? Muckenhoupt weights for which the discrete Hardy-Littlewood maximal operator is bounded on ?p w (Z+). The results will be proved b…
View article: Discrete Hardy's type inequalities and structure of discrete class of weights satisfy reverse Hölder's inequality
Discrete Hardy's type inequalities and structure of discrete class of weights satisfy reverse Hölder's inequality Open
In this paper, we will prove a new discrete weighted Hardy's type inequality with different powers.Next, we will apply this inequality to prove that the forward and backward propagation properties (self-improving properties) for the genera…
View article: Forced oscillation of conformable fractional partial delay differential equations with impulses
Forced oscillation of conformable fractional partial delay differential equations with impulses Open
In this paper, we establish some interval oscillation criteria for impulsive conformable fractional partial delay differential equations with a forced term. The main results will be obtained by employing Riccati technique. Our results exte…
View article: Some new generalized weighted dynamic inequalities of Hardy's type on time scales
Some new generalized weighted dynamic inequalities of Hardy's type on time scales Open
In this paper, we will prove some new generalized weighted dynamic inequalities of Hardy's type on a time scale T. The obtained results contain as special cases some published results when the time scale T = R and when T = N.The results, t…
View article: Half-linear dynamic equations and investigating weighted Hardy and Copson inequalities
Half-linear dynamic equations and investigating weighted Hardy and Copson inequalities Open
In this paper, we employ some algebraic equations due to Hardy and Littlewood to establish some conditions on weights in dynamic inequalities of Hardy and Copson type. For illustrations, we derive some dynamic inequalities of Wirtinger, Co…