On Ostrowski inequality for quantum calculus

Aljinović, Andrea Aglić; Kovačević, Domagoj; Puljiz, Mate; Keko, Ana Žgaljić

doi:10.1016/j.amc.2021.126454

Cited by 4 publications

(3 citation statements)

References 18 publications

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“…The classical concept of quantum calculus introduced in [20] has been extended and generalized in several directions. In quantum calculus H-H, Ostrowski-, Gruss-and Montgomery-type inequalities have been studied in numerous articles [21][22][23][24][25][26][27][28][29][30]. This topic has a number of applications in many fields of mathematics (number theory, combinatorics, orthogonal polynomials and hypergeometric functions) and also in physics and mathematics (mechanics and relativity theory) [31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Post-Quantum Integral Inequalities for Three-Times (p,q)-Differentiable Functions

Ciurdariu

Grecu

2023

Symmetry

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Section: Introductionmentioning

confidence: 99%

Post-Quantum Integral Inequalities for Three-Times (p,q)-Differentiable Functions

Ciurdariu

Grecu

2023

Symmetry

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“…In recent years, many researchers focused on the Ostrowski-type inequalities and their applications, see 2,3,4,5,6,7,8,9,10,11,12 and the references cited therein for more details. Specifically, many researchers worked on the Ostrowski-type inequalities and their applications using quantum calculus, some results can be found in 13,14,15,16,17,18,19,20,21 and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Post quantum Ostrowski-type inequalities for twice $(p,q)$-differentiable convex functions

Luangboon,

Nonlaopon,

Tariboon

et al. 2024

Preprint

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In this paper, we establish a new post quantum integral identity for twice $(p,q)$-differentiable convex functions. Then, we use this result to derive some new post quantum Ostrowski-type inequalities for twice $(p,q)$-differentiable convex functions involving $(p,q)_a$- and $(p,q)^b$-integrals. The newly established results are also proven to be generalizations of some existing results in the field of integral inequalities of already published ones.

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“…Convexity was used by Butt et al [30] to generate some new quantum Simpson-Newton-like estimates in the frame of Mercer type inequalities. Aljinović et al [31] established Ostrowski inequality for quantum calculus. Wang et al [32] developed new Ostrowski-type inequalities via q-fractional integrals involving s-convex functions.…”

Section: Introductionmentioning

confidence: 99%

Parameterized Quantum Fractional Integral Inequalities Defined by Using n-Polynomial Convex Functions

Liko

Srivástava

Mohammed

et al. 2022

Axioms

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Convexity performs the appropriate role in the theoretical study of inequalities according to the nature and behaviour. There is a strong relation between symmetry and convexity. In this article, we consider a new parameterized quantum fractional integral identity. Following that, our main results are established, which consist of some integral inequalities of Ostrowski and midpoint type pertaining to n-polynomial convex functions. From our main results, we discuss in detail several special cases. Finally, an example and an application to special means of positive real numbers are presented to support our theoretical results.

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On Ostrowski inequality for quantum calculus

Cited by 4 publications

References 18 publications

Post-Quantum Integral Inequalities for Three-Times (p,q)-Differentiable Functions

Post-Quantum Integral Inequalities for Three-Times (p,q)-Differentiable Functions

Post quantum Ostrowski-type inequalities for twice $(p,q)$-differentiable convex functions

Parameterized Quantum Fractional Integral Inequalities Defined by Using n-Polynomial Convex Functions

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