scholarly journals Some new generalizations of Maroni inequality on time scales

2013 ◽  
Vol 46 (4) ◽  
Author(s):  
Li Yin ◽  
Changjian Zhao
Keyword(s):  
Time Scales ◽  
Integral Inequalities ◽  
Special Cases

AbstractThe aim of present paper is to establish some new integral inequalities on time scales involving several functions and their derivatives which in the special cases yield the well known Maroni inequality and some of its generalizations.

scholarly journals Opial and Pólya Type Inequalities Via Convexity

2018 ◽  
Vol 60 (1) ◽  
pp. 145-159 ◽  
Author(s):  
S. H. Saker ◽  
D. M. Abdou ◽  
I. Kubiaczyk
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Hölder’S Inequality ◽  
Jensen’S Inequality ◽  
Chain Rule ◽  
Integral Inequalities ◽  
Taylor Formula ◽  
Special Cases ◽  
Discrete Inequalities ◽  
Classical Integral

Abstract In this paper, we prove some new dynamic inequalities related to Opial and Pólya type inequalities on a time scale 𝕋. We will derive the integral and discrete inequalities of Pólya’s type as special cases and also derive several classical integral inequalities of Opial’s type that has been obtained in the literature as special cases. The main results will be proved by using the chain rule, Hölder’s inequality and Jensen’s inequality, Taylor formula on time scales.

scholarly journals Steffensen-Type Inequalities with Weighted Function via (γ, a)-Nabla-Conformable Integral on Time Scales

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3046
Author(s):  
Ahmed A. El-Deeb ◽  
Jan Awrejcewicz
Keyword(s):  
Time Scales ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Weighted Function ◽  
Special Cases ◽  
Conformable Fractional Integral

The primary goal of this our research is to prove several new ∇-conformable dynamic Steffensen inequalities that were demonstrated in recent works. Our results generalize and extend existing results in the literature. Many special cases of the proposed results are obtained and analyzed such as new conformable fractional sum inequalities and new classical conformable fractional integral inequalities.

scholarly journals On nabla conformable fractional Hardy-type inequalities on arbitrary time scales

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed A. El-Deeb ◽  
Samer D. Makharesh ◽  
Eze R. Nwaeze ◽  
Olaniyi S. Iyiola ◽  
Dumitru Baleanu
Keyword(s):  
Present Article ◽  
Time Scales ◽  
Fractional Integral ◽  
Chain Rule ◽  
Integral Inequalities ◽  
Hardy Type Inequalities ◽  
Arbitrary Time ◽  
Hardy Type ◽  
Special Cases ◽  
Conformable Fractional Integral

AbstractThe main aim of the present article is to introduce some new ∇-conformable dynamic inequalities of Hardy type on time scales. We present and prove several results using chain rule and Fubini’s theorem on time scales. Our results generalize, complement, and extend existing results in the literature. Many special cases of the proposed results, such as new conformable fractional h-sum inequalities, new conformable fractional q-sum inequalities, and new classical conformable fractional integral inequalities, are obtained and analyzed.

scholarly journals A new generalization of some quantum integral inequalities for quantum differentiable convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yi-Xia Li ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Mujahid Abbas ◽  
Yu-Ming Chu
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
Quantum Integral ◽  
Special Cases

AbstractIn this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.

scholarly journals Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications

2021 ◽  
Vol 5 (3) ◽  
pp. 80
Author(s):  
Hari Mohan Srivastava ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Dumitru Baleanu ◽  
Y. S. Hamed
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Wright Function ◽  
Nonconvex Functions ◽  
Special Cases ◽  
Type Integral ◽  
Generic Class ◽  
Two Parameters ◽  
Class Of Functions

In this paper, the authors define a new generic class of functions involving a certain modified Fox–Wright function. A useful identity using fractional integrals and this modified Fox–Wright function with two parameters is also found. Applying this as an auxiliary result, we establish some Hermite–Hadamard-type integral inequalities by using the above-mentioned class of functions. Some special cases are derived with relevant details. Moreover, in order to show the efficiency of our main results, an application for error estimation is obtained as well.

scholarly journals Qi Type Diamond-Alpha Integral Inequalities

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 449
Author(s):  
Zhong-Xuan Mao ◽  
Ya-Ru Zhu ◽  
Bao-Hua Guo ◽  
Fu-Hai Wang ◽  
Yu-Hua Yang ◽  
...  
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Integral Inequalities

In this paper, we establish sufficient conditions for Qi type diamond-alpha integral inequalities and its generalized form on time scales.

scholarly journals New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1753
Author(s):  
Saima Rashid ◽  
Aasma Khalid ◽  
Omar Bazighifan ◽  
Georgia Irina Oros
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Type Inequality ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Convex Mappings ◽  
Special Cases ◽  
Harmonically Convex Functions

Integral inequalities for ℘-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented for ℘-convex functions via generalised fractional integral operator. A novel parameterized auxiliary identity involving generalised fractional integral is proposed for differentiable mappings. By using auxiliary identity, we derive several Ostrowski type inequalities for functions whose absolute values are ℘-convex mappings. It is presented that the obtained outcomes exhibit classical convex and harmonically convex functions which have been verified using Riemann–Liouville fractional integral. Several generalisations and special cases are carried out to verify the robustness and efficiency of the suggested scheme in matrices and Fox–Wright generalised hypergeometric functions.

scholarly journals Nonlinear integral inequalities on time scales with ‘maxima’

2014 ◽  
Vol 2014 (1) ◽  
pp. 255
Author(s):  
Phollakrit Thiramanus ◽  
Jessada Tariboon ◽  
Sotiris K Ntouyas
Keyword(s):  
Time Scales ◽  
Integral Inequalities

scholarly journals Some Nonlinear Delay Volterra–Fredholm Type Dynamic Integral Inequalities on Time Scales

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Yazhou Tian ◽  
A. A. El-Deeb ◽  
Fanwei Meng
Keyword(s):  
Time Scales ◽  
Qualitative Theory ◽  
Integral Inequalities ◽  
Dynamic Equations ◽  
Fredholm Type ◽  
Explicit Bounds ◽  
Theoretical Results ◽  
Nonlinear Delay

We are devoted to studying a class of nonlinear delay Volterra–Fredholm type dynamic integral inequalities on time scales, which can provide explicit bounds on unknown functions. The obtained results can be utilized to investigate the qualitative theory of nonlinear delay Volterra–Fredholm type dynamic equations. An example is also presented to illustrate the theoretical results.

Sign in / Sign up

Export Citation Format

Share Document