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 Synchronization Analysis of Multiple Integral Inequalities Driven by Steklov Operator

2021 ◽  
Vol 5 (3) ◽  
pp. 97
Author(s):  
Wedad Albalawi ◽  
Zareen A. Khan
Keyword(s):  
Integral Inequality ◽  
Hölder’S Inequality ◽  
Multiple Integral ◽  
Integral Inequalities ◽  
Integration By Parts ◽  
Hölder's Inequality ◽  
Steklov Operator

We construct a subclass of Copson’s integral inequality in this article. In order to achieve this goal, we attempt to use the Steklov operator for generalizing different inequalities of the Copson type relevant to the situations ρ>1 as well as ρ<1. We demonstrate the inequalities with the guidance of basic comparison, Holder’s inequality, and the integration by parts approach. Moreover, some new variations of Hardy’s integral inequality are also presented with the utilization of Steklov operator. We also formulate many remarks and two examples to show the novelty and authenticity of our results.

scholarly journals Some new generalizations of Hardy's integral inequality

2006 ◽  
Vol 2006 ◽  
pp. 1-15
Author(s):  
S. K. Sunanda ◽  
C. Nahak ◽  
S. Nanda
Keyword(s):  
Integral Inequality ◽  
Hölder’S Inequality ◽  
Hölder's Inequality

We have studied some new generalizations of Hardy's integral inequality using the generalized Holder's inequality.

scholarly journals General Raina fractional integral inequalities on coordinates of convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Dumitru Baleanu ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Badreddine Meftah
Keyword(s):  
Mathematical Model ◽  
Fractional Calculus ◽  
Convex Function ◽  
Mathematical Analysis ◽  
Integral Inequality ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Differentiable Functions ◽  
Special Cases

AbstractIntegral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In this study, authors have established some generalized Raina fractional integral inequalities using an $(l_{1},h_{1})$ ( l 1 , h 1 ) -$(l_{2},h_{2})$ ( l 2 , h 2 ) -convex function on coordinates. Also, we obtain an integral identity for partial differentiable functions. As an effect of this result, two interesting integral inequalities for the $(l_{1},h_{1})$ ( l 1 , h 1 ) -$(l_{2},h_{2})$ ( l 2 , h 2 ) -convex function on coordinates are given. Finally, we can say that our findings recapture some recent results as special cases.

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 A Note on Some Inequalities

1958 ◽  
Vol 4 (1) ◽  
pp. 7-15 ◽  
Author(s):  
T. M. Flett
Keyword(s):  
Fourier Series ◽  
Recent Work ◽  
Hölder’S Inequality ◽  
Integral Inequalities ◽  
Similar Nature ◽  
Hölder's Inequality

In the course of some recent work on Fourier series [5, 6] I had occasion to use a number of integral inequalities which were generalizations or limiting cases of known results. These inequalities may perhaps have other applications, and it seems worth while to collect them together in a separate note with one or two further results of a similar nature.For any number k, used as an index (exponent), and such that K > 1, we write k' = k′(k–1), so that k and k′ are conjugate indices in the sense of Hölder's inequality.

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 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.

scholarly journals A remark on local fractional calculus and ordinary derivatives

2016 ◽  
Vol 14 (1) ◽  
pp. 1122-1124 ◽  
Author(s):  
Ricardo Almeida ◽  
Małgorzata Guzowska ◽  
Tatiana Odzijewicz
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Short Note ◽  
General Definition ◽  
Local Fractional Derivative ◽  
Fundamental Properties ◽  
Local Fractional Calculus ◽  
Definition Of

AbstractIn this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.

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.

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