<abstract><p>In this paper, we establish some new dynamic Hardy-type inequalities with negative parameters on time scales nabla calculus by applying the reverse H ölder's inequality, integration parts, and chain rule calculus. As special cases of our results (when $ \mathbb{ T = R} $), get continuous analouges proven Benaissa Sarikaya, when \mathbb{T N}_{0} $, to best authors' knowledge are essentially new.</p></abstract>

<p>Some new reverse versions of Hilbert-type inequalities are studied in this paper. The results established by applying the time scale Hölder's inequality, Jensen's chain rule on scales, and mean inequality. As applications, some particular (when $ \mathbb{T = N} R} $) considered. Our provide estimates for these types improve those recently published literature.</p>

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

This paper provides novel generalizations by considering the generalized conformable fractional integrals for reverse Copson’s type inequalities on time scales. The main results will be proved using a general algebraic inequality, chain rule, Hölder’s and integration parts Our investigations unify extend some continuous their corresponding discrete analogues. In addition, when α = 1, we obtain well-known scale due to Hardy, Copson, Bennett, Leindler inequalities.

This paper is concerned with deriving some new dynamic Hilbert-type inequalities on time scales. The basic idea in proving the results using algebraic inequalities, Hölder’s inequality and Jensen’s inequality, As a special case of our results, we will obtain integrals their corresponding discrete Hilbert’s type.

This paper introduces novel generalizations of dynamic inequalities Copson type within the framework time scales delta calculus. The proposed leverage mathematical tools such as Hölder’s inequality, Minkowski’s chain rule on scales, and properties power rules scales. As special cases our results, particularly when scale T equals real line (T=R), we derive some classical continuous analogs previous inequalities. Furthermore, corresponds to set natural numbers including zero (T=N0), obtained...

This research investigates innovative extensions of Hardy-type inequalities through the use nabla Hölder’s and Jensen’s inequalities, combined with chain rule characteristics convex submultiplicative functions. We extend these within a cohesive framework that integrates elements both continuous discrete calculus. Furthermore, our study revisits specific integral from existing literature, showcasing wide-ranging relevance results.

Abstract Using the properties of superquadratic and subquadratic functions, we establish some new refinement multidimensional dynamic inequalities Hardy’s type on time scales. Our results contain recent related to classical Pólya–Knopp’s To show motivation paper, apply our obtain particular cases provide refinements Hardy-type known in literature.

Throughout this article, we will demonstrate some new generalizations of dynamic Hilbert type inequalities, which are used in various problems involving symmetry. We develop a number those symmetric inequalities to general time scale. From these as particular cases, formulate integral and discrete that have been demonstrated the literature also extend achieved scales.

Within this paper, we derive entire series of new Hilbert and Hardy-Hilbert form integral inequalities with non-conjugate exponents on time scales. Firstly, demonstrate discuss two general equivalent type, as well their corresponding reverse inequalities. We also extend in most form. The results obtained are then applied to a kernel special Hardy Our cases some the dynamic achieved scales include when T=R.

By utilizing the precepts related to punctuation of time scales <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi mathvariant="double-struck">T</mml:mi></mml:math>, we present some nouveau forms in quotients for Hardy’s and inequalities on scales. In particular, recent results Pólya-Knopp, Hardy-Hilbert, Hardy-Littlewood-Pólya-type are presented.

This paper is interested in establishing some new reverse Hilbert-type inequalities, by using chain rule on time scales, Jensen’s, and Hölder’s with Specht’s ratio mean inequalities. To get the results, we used function its applications for inequalities of Hilbert-type. Symmetrical properties play an essential role determining correct methods to solve The special cases yield recent relevance, which also provide estimates these type.

In this paper, we study the inequalities of Hardy–Knopp type with kernel functions which have two nonnegative different weighted in spaces, a general domain called time scale calculus. A calculus is considered as unification continuous and discrete We will prove these to avoid proving them twice once case second case. Also, special cases calculus, can some new domains. Our results be proved by using definition Hardy operator on scale. These (when ) are essentially new.

In this article, some fractional Hardy-Leindler-type inequalities will be illustrated by utilizing the chain law, Hölder’s inequality, and integration parts on time scales. As a result of this, classical integral obtained. Also, we would have variety well-known dynamic as special cases from our outcomes when <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>α</a:mi> <a:mo>=</a:mo> <a:mn>1</a:mn> </a:math> .

Abstract In this paper, we will prove some fundamental properties of the power mean operator $$ \mathcal{M}_{p}g(t)= \biggl( \frac{1}{\Upsilon(t)} \int _{0}^{t} \lambda (s)g^{p} ( s ) \,ds \biggr) ^{1/p},\quad\text{for }t\in \mathbb{I}\subseteq \mathbb{R}_{+}, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:mi>g</mml:mi> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow>...

In this paper, we derive some new fractional extensions of Hardy’s type inequalities. The corresponding reverse relations are also obtained by using the conformable calculus from which classical integral inequalities deduced as special cases at α=1.

This manuscript develops the study of reverse Hilbert-type inequalities by applying Hölder on T. We generalize inequality with power two replacing a new β,β&gt;1. The main results are proved using Specht’s ratio, chain rule and Jensen’s inequality. Our (when T=N) essentially new. Symmetrical properties play an essential role in determining correct methods to solve inequalities.

In this article, we establish several new generalized Hardy-type inequalities involving functions on time-scale nabla calculus. Furthermore, derive some multidimensional time scales The main results are proved by applying Minkowski’s inequality, Jensen’s inequality and Arithmetic Mean–Geometric Mean inequality. As a special case of our results, when T=R, obtain refinements well-known continuous T=N, the which essentially new.

In this article, we discuss several novel generalized Ostrowski-type inequalities for functions whose derivative module is relatively convex in time scales calculus. Our core findings are proved by using the integration parts technique, Hölder’s inequality, and chain rule on scales. These derived expand existing literature, enriching specific integral within domain.

This paper introduced novel multidimensional Hardy-type inequalities with general kernels on time scales, extending existing results in the literature. We established generalized involving a Hardy operator multiple variables and arbitrary scales. Our findings not only encompassed known realm of real numbers ($ \mathbb{T=R} $), but also provided refinements generalizations thereof. The proposed offered versatile applications mathematical analysis beyond, contributing to ongoing exploration diverse

&lt;p&gt;The oscillation property of third-order differential equations with non-positive neutral coefficients is discussed. New sufficient conditions are provided to guarantee that every solution the considered equation almost oscillatory. Both canonical and non-canonical cases considered. Illustrative examples introduced support obtained results.&lt;/p&gt;

This study develops the of reverse Hilbert‐type inequalities on time scales where we can establish some new generalizations via supermultiplicative functions by applying Hölder inequalities. The main results will be proved using Specht’s ratio, chain rule, and Jensen’s inequality. Our (when ) are essentially new.