Some Quantum Integral Inequalities Based on Left-Right Quantum Integrals

Kunt, Mehmet; Baidar, Abdul Wakil; Şanlı, Zeynep

doi:10.55525/tjst.1112582

Cited by 3 publications

(1 citation statement)

References 15 publications

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“…It is shown in the video that the alternative definition introduces some simplicity in determining the derivatives of some of the well-known functions. The quantum derivative, which is similar to (5), is used by physicists with the expression being 𝑓𝑓(𝑞𝑞𝑥𝑥)−𝑓𝑓(𝑥𝑥) 𝑞𝑞𝑥𝑥−𝑥𝑥 without the limiting process (Kunt et al, 2022). Another generalization of the usual derivative is the fractal derivatives in which the derivative operation consists of fractional repetitions rather than integers.…”

Section: 𝜀𝜀mentioning

confidence: 99%

Generalized Definition of the Derivative

Pakdemirli

2024

Preprint

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The classical limit definition of a derivative is expressed in a more general form. The general form includes two arbitrary functions of the parameter for which the limit is calculated. A special case of the general form, which includes scaling and translational symmetry transformations of the limiting parameter, is also discussed. The errors in using the classical definition and the generalized form are calculated for small values of the limiting parameter. The derivatives of some known functions are proven using the new definition. For some well-known functions, a suitable selection of the generalized form may introduce simplicity in calculating the derivatives.

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Section: 𝜀𝜀mentioning

confidence: 99%

Generalized Definition of the Derivative

Pakdemirli

2024

Preprint

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Properties and Applications of Symmetric Quantum Calculus

Vivas-Cortez,

Javed,

Awan

et al. 2024

Fractal Fract

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Symmetric derivatives and integrals are extensively studied to overcome the limitations of classical derivatives and integral operators. In the current investigation, we explore the quantum symmetric derivatives on finite intervals. We introduced the idea of right quantum symmetric derivatives and integral operators and studied various properties of both operators as well. Using these concepts, we deliver new variants of Young’s inequality, Hölder’s inequality, Minkowski’s inequality, Hermite–Hadamard’s inequality, Ostrowski’s inequality, and Gruss–Chebysev inequality. We report the Hermite–Hadamard’s inequalities by taking into account the differentiability of convex mappings. These fundamental results are pivotal to studying the various other problems in the field of inequalities. The validation of results is also supported with some visuals.

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Symmetric quantum calculus in interval valued frame work: operators and applications

Wang,

Javed,

Awan

et al. 2024

MATH

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<p>The primary emphasis of the present study is to introduce some novel characterizations of the interval-valued $ (\mathcal{I}.\mathcal{V}) $ right symmetric quantum derivative and antiderivative operators relying on generalized Hukuhara difference. To continue the study, we start with the concept of symmetric differentiability in the interval-valued sense and explore some important properties. Furthermore, through the utilization of the $ (\mathcal{I}.\mathcal{V}) $ symmetric derivative operator, we develop the right-sided $ (\mathcal{I}.\mathcal{V}) $ integral operator and explore its key properties. Also, we establish various $ (\mathcal{I}.\mathcal{V}) $ trapezium-like inequalities by considering the newly proposed operators and support line. Later on, we deliver another proof of the trapezium inequality through an analytical approach. Also, we present the numerical and visual analysis for the verification of our results.</p>

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Some Quantum Integral Inequalities Based on Left-Right Quantum Integrals

Cited by 3 publications

References 15 publications

Generalized Definition of the Derivative

Generalized Definition of the Derivative

Properties and Applications of Symmetric Quantum Calculus

Symmetric quantum calculus in interval valued frame work: operators and applications

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