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The Inequalities for Some Types of q-Integrals [article]

Predrag M. Rajkovic, Sladjana D. Marinkovic, Miomir S. Stankovic
2006 arXiv   pre-print
We discuss the inequalities for q-integrals because of the fact that the inequalities can be very useful in the future mathematical research.  ...  Since q-integral of a function over an interval [a,b] is defined by the difference of two infinite sums, there a lot of unexpected troubles in analyzing analogs of well-known integral inequalities.  ...  At last, we give a few new inequalities which are valid only for some types of the q-integrals.  ... 
arXiv:math/0605208v1 fatcat:irazsqxbjraitdz3zbt5jxad7u

The inequalities for some types of q-integrals

Sladjana Marinković, Predrag Rajković, Miomir Stanković
2008 Computers and Mathematics with Applications  
Using the restriction of the q-integral over [a, b] to a finite sum and q-integral of Riemann-type, we establish new integral inequalities of q-Chebyshev type, q-Grüss type, q-Hermite-Hadamard type and  ...  Some inequalities which include the boundaries of functions are also indicated.  ...  Acknowledgements The author wishes to thank the referees for their helpful suggestions.  ... 
doi:10.1016/j.camwa.2008.05.035 fatcat:tkmwl5b4czgb7nxjjjy4f4xao4

On some new quantum midpoint-type inequalities for twice quantum differentiable convex functions

Muhammad Aamir Ali, Necmettin Alp, Hüseyin Budak, Yu-Ming Chu, Zhiyue Zhang
2021 Open Mathematics  
The present paper aims to find some new midpoint-type inequalities for twice quantum differentiable convex functions.  ...  The consequences derived in this paper are unification and generalization of the comparable consequences in the literature on midpoint inequalities.  ...  1 Acknowledgment: The authors would like to express their sincere thanks to the editor and the anonymous reviewers for their helpful comments and suggestions.  ... 
doi:10.1515/math-2021-0015 fatcat:prkwny24anh7rdy4rjlhjjreze

Some New Poincaré-type inequalities

Wing-Sum Cheung
2001 Bulletin of the Australian Mathematical Society  
New and improved Poincare-type integral inequalities involving many functions of many variables are established.  ...  These in turn can serve as generators and can generate numerous Poincare-type integral inequalities by choosing different parameters.  ...  types of integral inequalities like Wirtinger-type integral inequalities 322 W-S.  ... 
doi:10.1017/s0004972700019365 fatcat:eibnvzxa25d4xbvzlxbv3jwwqm

Some new integral inequalities of the Simpson type for MT-convex functions

Siqintuya JİN, Wan AYİNG, Bai-ni GUO
2022 Advances in the Theory of Nonlinear Analysis and its Applications  
In the paper, with the aid of a known integral identity, the authors establish some new inequalities, similar to the celebrated Simpson's integral inequality, for dierentiable MT-convex functions.  ...  Acknowledgements The authors thank anonymous referees for their careful reading and valuable comments on the original version of this paper.  ...  Conicts of Interest The authors declare no conict of interest.  ... 
doi:10.31197/atnaa.1003964 fatcat:txyyavvdcfgfvjshitajhineyy

INVESTIGATION OF SOME RESULTS ARISING FROM POST QUANTUM CALCULUS

GHAZALA GULSHAN, RASHIDA HUSSAIN, ASGHAR ALI
2020 Journal of Science and Arts  
Some special cases of the (p,q)-midpoint, Simpson, Averaged midpoint trapezoid, and trapezoid type integral identities are also derived.  ...  The purpose of this paper is to establish different type of identities for (p,q)-calculus.  ...  Furthermore, they obtained some new result for the the (p,q)-calculus of several important integral inequalities.  ... 
doi:10.46939/j.sci.arts-20.3-a06 fatcat:nciytx5yubd2bbdhmfx7v7o5wi

Montgomery identity and Ostrowski-type inequalities via quantum calculus

Thanin Sitthiwirattham, Muhammad Aamir Ali, Huseyin Budak, Mujahid Abbas, Saowaluck Chasreechai
2021 Open Mathematics  
In this paper, we prove a quantum version of Montgomery identity and prove some new Ostrowski-type inequalities for convex functions in the setting of quantum calculus.  ...  Moreover, we discuss several special cases of newly established inequalities and obtain different new and existing inequalities in the field of integral inequalities.  ...  Conflict of interest: The authors state no competing interests. Montgomery identity and Ostrowski-type inequalities  1107  ... 
doi:10.1515/math-2021-0088 fatcat:ukr7rozfcrht7ghr7robn55l4m

Special Issue Editorial "Symmetry in the Mathematical Inequalities"

Nicuşor Minculete
2022 Symmetry  
The theory of inequalities represents a long-standing topic in many mathematical areas and remains an attractive research domain with many applications [...]  ...  Conflicts of Interest: The author declares no conflict of interest.  ...  ., in the paper "On Some New Simpson's Formula Type Inequalities for Convex Functions in Post-Quantum Calculus" [16] , proved a new (p, q)-integral identity involving a (p, q)-derivative and (p, q)-integral  ... 
doi:10.3390/sym14040774 fatcat:pkug4ogogzbzncu5zc3p2m3p7q

Riemann–Liouville Fractional Newton's Type Inequalities for Differentiable Convex Functions

Thanin Sitthiwirattham, Kamsing Nonlaopon, Muhammad Aamir Ali, Hüseyin Budak
2022 Fractal and Fractional  
In this paper, we prove some new Newton's type inequalities for differentiable convex functions through the well-known Riemann–Liouville fractional integrals.  ...  Moreover, we prove some inequalities of Riemann–Liouville fractional Newton's type for functions of bounded variation.  ...  We thanks to worthy referees and editor for their valuable comments. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/fractalfract6030175 fatcat:iuwyh3estrhhhaiu73g3scnhi4

Ting type inequality for Sugeno integrals

Dug Hun Hong, Jae Duck Kim
2018 Applied Mathematical Sciences  
This paper propose a Ting type inequality for the Sugeno integrals. That is, we show that H p,q ≤ (S)  ...  This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1B027869).  ...  [13] [14] [15] presented several new types of inequalities for Sugeno integrals, including a Prekopa-Leindler type inequality, a Jensen type inequality, and some convolution type inequalities.  ... 
doi:10.12988/ams.2018.810153 fatcat:4yldphvrjbb7rdcp6asoxgbktm

Quantum Ostrowski-type inequalities for twice quantum differentiable functions in quantum calculus

Muhammad Aamir Ali, Hüseyin Budak, Abdullah Akkurt, Yu-Ming Chu
2021 Open Mathematics  
Then, by utilizing the convexity of ∣ D q 2 b f ∣ | {}^{b}D_{q}^{2}\hspace{0.08em}f| and ∣ D q 2 a f ∣ | {}_{a}D_{q}^{2}\hspace{0.08em}f| , we establish some quantum Ostrowski inequalities for twice quantum  ...  The results presented here are the generalization of already published ones.  ...  Acknowledgments: The authors would like to express their sincere thanks to the editor and the anonymous reviewers for their helpful comments and suggestions.  ... 
doi:10.1515/math-2021-0020 fatcat:zusyfc4qj5bzdfaq4oxjtwdoze

On Poincaré-type integral inequalities

B.G Pachpatte
1986 Journal of Mathematical Analysis and Applications  
The aim of the present paper is to establish some multidimensional Poincark-type integral inequalities involving two functions and their first order partial derivatives.  ...  Our analysis is more elementary and provide easy proofs of some Poincark type integral inequalities.  ...  ACKNOWLEDGMENT The author acknowledge with thanks the helpful suggestions made by the referee for the improvement of this paper.  ... 
doi:10.1016/0022-247x(86)90069-7 fatcat:a5wuabvhujawngfyckudnzxfbq

Page 7754 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
Summary: “Some variants of one-dimensional and two- dimensional integral inequalities of the Volterra type are applied to study behaviour properties of solutions to various boundary value problems for  ...  The authors study in compact sets Q C R” integrals of the follow- ing type: Lg) = | el?" fixjdx, g>0; 0<-f(x) <1.  ... 

Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals via s-convex functions and applications to special means

Jinrong Wang, Xuezhu Li, Yong Zhou
2016 Filomat  
In this paper, we establish some new Hermite-Hadamard type inequalities involving Riemann-Liouville fractional integrals via s-convex functions in the second sense.  ...  Meanwhile, we present many useful estimates on these types of new Hermite-Hadamard type inequalities. Some applications to special means of real numbers are given.  ...  Acknowledgements The authors thank the referees for their careful reading of the manuscript and insightful comments, which helped to improve the quality of the paper.  ... 
doi:10.2298/fil1605143w fatcat:io22cyifgfcu5km6xemgw5jrwe

A survey on the study of Hilbert-type inequalities

Qiang Chen, Bicheng Yang
2015 Journal of Inequalities and Applications  
In this paper, we give a summary of the development of the theory of Hilbert-type inequalities during the past 110 years. MSC: 26D15; 47A07  ...  Hilbert-type inequalities are divided three parts: Hilbert's inequalities (1908), Hardy-Hilbert-type inequalities (1934) and Yang-Hilbert-type inequalities (2009).  ...  Acknowledgements The authors wish to express their thanks to the referees for their careful reading of the manuscript and for their valuable suggestions.  ... 
doi:10.1186/s13660-015-0829-7 fatcat:f56u5jagnnchxe62a3q2u6yliu
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