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 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.

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.

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 A Local Fractional Integral Inequality on Fractal Space Analogous to Anderson’s Inequality

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Wei Wei ◽  
H. M. Srivastava ◽  
Yunyi Zhang ◽  
Lei Wang ◽  
Peiyi Shen ◽  
...  
Keyword(s):  
Integral Inequality ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Local Fractional Integral ◽  
Fractal Space ◽  
Integral Analogue

Anderson's inequality (Anderson, 1958) as well as its improved version given by Fink (2003) is known to provide interesting examples of integral inequalities. In this paper, we establish local fractional integral analogue of Anderson's inequality on fractal space under some suitable conditions. Moreover, we also show that the local fractional integral inequality on fractal space, which we have proved in this paper, is a new generalization of the classical Anderson's inequality.

scholarly journals Hilbert-type inequalities for time scale nabla calculus

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
H. M. Rezk ◽  
Ghada AlNemer ◽  
H. A. Abd El-Hamid ◽  
Abdel-Haleem Abdel-Aty ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Time Scale ◽  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Arbitrary Time ◽  
Hilbert Type

Abstract This paper deals with the derivation of some new dynamic Hilbert-type inequalities in time scale nabla calculus. In proving the results, the basic idea is to use some algebraic inequalities, Hölder’s inequality, and Jensen’s time scale inequality. This generalization allows us not only to unify all the related results that exist in the literature on an arbitrary time scale, but also to obtain new outcomes that are analytical to the results of the delta time scale calculation.

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