scholarly journals Some new Opial type dynamic inequalities via convex functions and applications

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. H. Saker ◽  
J. Alzabut ◽  
A. G. Sayed ◽  
D. O’Regan
Keyword(s):  
Time Scales ◽  
Convex Functions ◽  
Chain Rule ◽  
Convexity Property

AbstractIn 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 some particular Opial-type inequalities reported in the literature.

scholarly journals Some Opial Dynamic Inequalities Involving Higher Order Derivatives on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Samir H. Saker
Keyword(s):  
Time Scales ◽  
Hölder’S Inequality ◽  
Higher Order ◽  
Chain Rule ◽  
Simple Consequence ◽  
Hölder's Inequality ◽  
Special Cases ◽  
Discrete Inequalities

We will prove some new Opial dynamic inequalities involving higher order derivatives on time scales. The results will be proved by making use of Hölder's inequality, a simple consequence of Keller's chain rule and Taylor monomials on time scales. Some continuous and discrete inequalities will be derived from our results as special cases.

scholarly journals Some new inequalities via s-convex functions on time scales

2021 ◽  
Vol 13 (1) ◽  
pp. 239-257
Author(s):  
Naila Mehreen ◽  
Matloob Anwar
Keyword(s):  
Convex Function ◽  
Time Scales ◽  
Convex Functions ◽  
Time Scale ◽  
Integral Inequalities ◽  
New Inequalities

Abstract In this paper, we prove some new integral inequalities for s-convex function on time scale. We give results for the case when time scale is ℝ and when time scale is ℕ.

scholarly journals Weighted dynamic inequalities of Opial-type on time scales

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
A. A. El-Deeb ◽  
Fatma M. Kh ◽  
Gamal A. F. Ismail ◽  
Zareen A. Khan
Keyword(s):  
Time Scales ◽  
Hölder Inequality ◽  
Chain Rule ◽  
Simple Consequence ◽  
Special Cases ◽  
Discrete Inequalities

Abstract In this paper, we will state and prove some weighted dynamic inequalities of Opial-type involving integrals of powers of a function and of its derivative on time scales which not only extend some results in the literature but also improve some of them. The main results will be proved by using some algebraic inequalities, the Hölder inequality and a simple consequence of Keller’s chain rule on time scales. As special cases of the obtained dynamic inequalities, we will get some continuous and discrete inequalities.

SOME REVERSE DYNAMIC INEQUALITIES ON TIME SCALES

2017 ◽  
Vol 96 (3) ◽  
pp. 445-454 ◽  
Author(s):  
R. P. AGARWAL ◽  
R. R. MAHMOUD ◽  
D. O’REGAN ◽  
S. H. SAKER
Keyword(s):  
Time Scales ◽  
Hölder Inequality ◽  
Chain Rule ◽  
Fubini Theorem ◽  
Reverse Hölder Inequality ◽  
Reverse Hölder

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.

scholarly journals Extensions of Hermite–Hadamard inequalities for harmonically convex functions via generalized fractional integrals

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Xue-Xiao You ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Praveen Agarwal ◽  
Yu-Ming Chu
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Convexity Property ◽  
Hadamard Inequality ◽  
Harmonically Convex Functions ◽  
Harmonic Convexity

AbstractIn the paper, the authors establish some new Hermite–Hadamard type inequalities for harmonically convex functions via generalized fractional integrals. Moreover, the authors prove extensions of the Hermite–Hadamard inequality for harmonically convex functions via generalized fractional integrals without using the harmonic convexity property for the functions. The results offered here are the refinements of the existing results for harmonically convex functions.

scholarly journals Some new dynamic inequalities with several functions of Hardy type on time scales

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Adnane Hamiaz ◽  
Waleed Abuelela ◽  
Samir H. Saker ◽  
Dumitru Baleanu
Keyword(s):  
Time Scales ◽  
Hölder’S Inequality ◽  
Chain Rule ◽  
Integration By Parts ◽  
Hölder's Inequality ◽  
Hardy Type ◽  
Do So

AbstractThe aim of this article is to prove some new dynamic inequalities of Hardy type on time scales with several functions. Our results contain some results proved in the literature, which are deduced as limited cases, and also improve some obtained results by using weak conditions. In order to do so, we utilize Hölder’s inequality, the chain rule, and the formula of integration by parts on time scales.

scholarly journals Subdifferentials of convex functions on time scales

2011 ◽  
Vol 29 (2) ◽  
pp. 671-691
Author(s):  
Małgorzata Wyrwas ◽  
◽  
Dorota Mozyrska ◽  
Ewa Girejko ◽  
Keyword(s):  
Time Scales ◽  
Convex Functions

scholarly journals Generalizations of the Jensen functional involving diamond integrals via Abel–Gontscharoff interpolation

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Rabia Bibi ◽  
Ammara Nosheen ◽  
Shanaz Bano ◽  
Josip Pečarić
Keyword(s):  
Time Scales ◽  
Convex Functions ◽  
Jensen Inequality ◽  
Jensen Functional

AbstractIn this paper we obtain several refinements of the Jensen inequality on time scales by generalizing Jensen’s functional for n-convex functions. We also investigate the bounds for the identities related to the new improvements obtained.

scholarly journals Estimation of divergences on time scales via the Green function and Fink’s identity

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Iqrar Ansari ◽  
Khuram Ali Khan ◽  
Ammara Nosheen ◽  
Ðilda Pečarić ◽  
Josip Pečarić
Keyword(s):  
Green Function ◽  
Time Scales ◽  
Convex Functions ◽  
Quantum Calculus ◽  
Divergence Measures ◽  
The Green Function ◽  
Fink’S Identity

AbstractThe aim of the present paper is to obtain new generalizations of an inequality for n-convex functions involving Csiszár divergence on time scales using the Green function along with Fink’s identity. Some new results in h-discrete calculus and quantum calculus are also presented. Moreover, inequalities for some divergence measures are also deduced.

scholarly journals Hardy-Type Inequalities on Time Scale via Convexity in Several Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Tzanko Donchev ◽  
Ammara Nosheen ◽  
Josip Pečarić
Keyword(s):  
Time Scales ◽  
Convex Functions ◽  
Time Scale ◽  
Hardy Type Inequalities ◽  
Arbitrary Time ◽  
Hardy Type ◽  
Several Variables ◽  
New Inequalities

We extend some Hardy-type inequalities with general kernels to arbitrary time scales using multivariable convex functions. Some classical and new inequalities are deduced seeking applications.

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