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 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 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.

scholarly journals SOME HARDY-TYPE INEQUALITIES FOR CONVEX FUNCTIONS VIA DELTA FRACTIONAL INTEGRALS

Fractals ◽  
2021 ◽  
pp. 2240004
Author(s):  
FUZHANG WANG ◽  
USAMA HANIF ◽  
AMMARA NOSHEEN ◽  
KHURAM ALI KHAN ◽  
HIJAZ AHMAD ◽  
...  
Keyword(s):  
Fractional Calculus ◽  
Time Scales ◽  
Convex Functions ◽  
Type Inequality ◽  
Fractional Integrals ◽  
Discrete Fractional Calculus ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Hilbert Type

In this paper, some Jensen- and Hardy-type inequalities for convex functions are extended by using Riemann–Liouville delta fractional integrals. Further, some Pólya–Knopp-type inequalities and Hardy–Hilbert-type inequality for convex functions are also proved. Moreover, some related inequalities are proved by using special kernels. Particular cases of resulting inequalities provide the results on fractional calculus, time scales calculus, quantum fractional calculus and discrete fractional calculus.

scholarly journals Estimation of divergence measures on time scales via Taylor’s polynomial and Green’s function with applications in q-calculus

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

AbstractTaylor’s polynomial and Green’s function are used to obtain new generalizations of an inequality for higher order convex functions containing Csiszár divergence on time scales. Various new inequalities for some divergence measures in quantum calculus and h-discrete calculus are also established.

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 New Weighted Opial-Type Inequalities on Time Scales for Convex Functions

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 842
Author(s):  
Ahmed A. El-Deeb ◽  
Dumitru Baleanu
Keyword(s):  
Time Scales ◽  
Convex Functions ◽  
Time Scale ◽  
Hölder Inequality ◽  
Special Cases ◽  
Discrete Inequalities ◽  
General Time

Our work is based on the multiple inequalities illustrated in 1967 by E. K. Godunova and V. I. Levin, in 1990 by Hwang and Yang and in 1993 by B. G. Pachpatte. With the help of the dynamic Jensen and Hölder inequality, we generalize a number of those inequalities to a general time scale. In addition to these generalizations, some integral and discrete inequalities will be obtained as special cases of our results.

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