scholarly journals Some Further Generalizations of Hölder's Inequality and Related Results on Fractal Space

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Guang-Sheng Chen ◽  
H. M. Srivastava ◽  
Pin Wang ◽  
Wei Wei
Keyword(s):  
Fractional Integral ◽  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Special Cases ◽  
Local Fractional Integral ◽  
Fractal Space

We establish some new generalizations and refinements of the local fractional integral Hölder’s inequality and some related results on fractal space. We also show that many existing inequalities related to the local fractional integral Hölder’s inequality are special cases of the main inequalities which are presented here.

A Subdividing of Local Fractional Integral Holder’s Inequality on Fractal Space

2014 ◽  
Vol 998-999 ◽  
pp. 976-979
Author(s):  
Guang Sheng Chen
Keyword(s):  
Fractional Integral ◽  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Local Fractional Integral ◽  
Fractal Space

In this paper, we establish a subdividing of Hölder’s inequality via local fractional integral. Its reverse version is also given.

scholarly journals Hermite-Hadamard type inequalities for generalized convex functions on fractal sets style

2018 ◽  
Vol 38 (1) ◽  
pp. 101-116 ◽  
Author(s):  
Muharrem Tomar ◽  
Praveen Agarwal ◽  
Junesang Choi
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Generalized Convex Functions ◽  
Fractal Sets ◽  
Special Cases ◽  
Logarithmic Means ◽  
Local Fractional Integral ◽  
Generalized Arithmetic

We aim to  establish certain generalized Hermite-Hadamard's inequalities for generalized convex functions via local fractional integral. As special cases of some of the results presented here, certain interesting inequalities involving generalized arithmetic and logarithmic means are obtained.

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.

Applications of Yang-Fourier Transform to Local Fractional Equations with Local Fractional Derivative and Local Fractional Integral

2012 ◽  
Vol 461 ◽  
pp. 306-310 ◽  
Author(s):  
Wei Ping Zhong ◽  
Feng Gao ◽  
Xiao Ming Shen
Keyword(s):  
Fourier Transform ◽  
Fractional Derivative ◽  
Fractional Integral ◽  
Fractional Fourier Transform ◽  
Local Fractional Derivative ◽  
Fractional Equations ◽  
Local Fractional Integral ◽  
Fractal Space

Yang-Fourier transform is the generalization of the fractional Fourier transform of non-differential functions on fractal space. In this paper, we show applications of Yang-Fourier transform to local fractional equations with local fractional derivative and local fractional integral

scholarly journals New Variant of Hermite–Jensen–Mercer Inequalities via Riemann–Liouville Fractional Integral Operators

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Qiong Kang ◽  
Saad Ihsan Butt ◽  
Waqas Nazeer ◽  
Mehroz Nadeem ◽  
Jamshed Nasir ◽  
...  
Keyword(s):  
Fractional Integral ◽  
Hölder’S Inequality ◽  
Integral Operators ◽  
Differentiable Mapping ◽  
Fractional Integral Operators ◽  
Hölder's Inequality ◽  
Differentiable Functions ◽  
New Variant ◽  
The Absolute

In this paper, certain Hermite–Hadamard–Mercer-type inequalities are proved via Riemann–-Liouville fractional integral operators. We established several new variants of Hermite–Hadamard’s inequalities for Riemann–Liouville fractional integral operators by utilizing Jensen–Mercer inequality for differentiable mapping ϒ whose derivatives in the absolute values are convex. Moreover, we construct new lemmas for differentiable functions ϒ′, ϒ″, and ϒ‴ and formulate related inequalities for these differentiable functions using variants of Hölder’s inequality.

scholarly journals Generalizations of Hölder’s and Some Related Integral Inequalities on Fractal Space

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Guang-Sheng Chen
Keyword(s):  
Fractional Calculus ◽  
Integral Inequality ◽  
Hölder’S Inequality ◽  
Integral Inequalities ◽  
Hölder's Inequality ◽  
Local Fractional Calculus ◽  
Related Integral ◽  
Fractal Space

Based on the local fractional calculus, we establish some new generalizations of Hölder’s inequality. By using it, some related results on the generalized integral inequality in fractal space are investigated in detail.

scholarly journals Generalized fractal Jensen and Jensen–Mercer inequalities for harmonic convex function with applications

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Saad Ihsan Butt ◽  
Praveen Agarwal ◽  
Saba Yousaf ◽  
Juan L. G. Guirao
Keyword(s):  
Probability Density Function ◽  
Convex Function ◽  
Fractional Integral ◽  
Type Inequality ◽  
Fractional Integrals ◽  
Fractal Sets ◽  
Local Fractional Integral ◽  
Fractal Space ◽  
Harmonic Convex ◽  
Harmonically Convex Function

AbstractIn this paper, we present a generalized Jensen-type inequality for generalized harmonically convex function on the fractal sets, and a generalized Jensen–Mercer inequality involving local fractional integrals is obtained. Moreover, we establish some generalized Jensen–Mercer-type local fractional integral inequalities for harmonically convex function. Also, we obtain some generalized related results using these inequalities on the fractal space. Finally, we give applications of generalized means and probability density function.

scholarly journals More on Hölder’s Inequality and It’s Reverse via the Diamond-Alpha Integral

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1716
Author(s):  
M. Zakarya ◽  
H. A. Abd El-Hamid ◽  
Ghada AlNemer ◽  
H. M. Rezk
Keyword(s):  
Linear Combination ◽  
Time Scales ◽  
Time Scale ◽  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Special Cases ◽  
General Time

In this paper, we investigate some new generalizations and refinements for Hölder’s inequality and it’s reverse on time scales through the diamond-α dynamic integral, which is defined as a linear combination of the delta and nabla integrals, which are used in various problems involving symmetry. We develop a number of those symmetric inequalities to a general time scale. Our results as special cases extend some integral dynamic inequalities and Qi’s inequalities achieved on time scales and also include some integral disparities as particular cases when T=R.

An Improvement of Local Fractional Integral Minkowski’s Inequality on Fractal Space

2014 ◽  
Vol 998-999 ◽  
pp. 980-983
Author(s):  
Guang Sheng Chen
Keyword(s):  
Fractional Integral ◽  
Minkowski’S Inequality ◽  
Local Fractional Integral ◽  
Fractal Space

In the paper, we establish some improvements of Minkowski’s inequality on fractal space via the local fractional integral.

scholarly journals Some fractional dynamic inequalities on time scales of Hardy's type

2020 ◽  
Vol 23 (02) ◽  
pp. 98-109
Author(s):  
A. G. Sayed ◽  
S. H. Saker ◽  
A. M. Ahmed
Keyword(s):  
Time Scales ◽  
Hölder’S Inequality ◽  
Chain Rule ◽  
Integration By Parts ◽  
Hölder's Inequality ◽  
Special Cases

In this paper, we prove some new fractional dynamic inequalities on time scales of Hardy's type due to Yang and Hwang. The results will be proved by employing the chain rule, Hölder's inequality, and integration by parts on fractional time scales. Several well-known dynamic inequalities on time scales will be obtained as special cases from our results.

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