(q1,q2)-Trapezium-Like Inequalities Involving Twice Differentiable Generalized m-Convex Functions and Applications

Awan, Muhammad Uzair; Javed, Muhammad Zakria; Slimane, Ibrahim; Kashuri, Artion; Cesarano, Clemente; Nonlaopon, Kamsing

doi:10.3390/fractalfract6080435

Cited by 3 publications

(2 citation statements)

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“…In Ref. [11], the authors focused on establishing the post-quantum analogues of trapezium inequality via generalized m-convex mappings. Duo et al [12] analyzed some quantum estimates through a unified approach to obtain several type inequalities by specifying the values for parameters.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

Properties and Applications of Symmetric Quantum Calculus

Vivas-Cortez,

Javed,

Awan

et al. 2024

Fractal Fract

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“…Inequalities have increasing importance in modern mathematical analysis, and in many other mathematical disciplines. Moreover, it seems to have "a pivotal role in several pure and applied sciences" [1]. Integral inequalities, on the other hand, "plays a vital role in the theory of differential equations" [2].…”

Section: Introductionmentioning

confidence: 99%

New Perspectives of Symmetry Conferred by q-Hermite-Hadamard Type Integral Inequalities

Ciurdariu,

Grecu

2023

Symmetry

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The main goal of this work is to provide quantum parametrized Hermite-Hadamard like type integral inequalities for functions whose second quantum derivatives in absolute values follow different type of convexities. A new quantum integral identity is derived for twice quantum differentiable functions, which is used as a key element in our demonstrations along with several basic inequalities such as: power mean inequality, and Holder’s inequality. The symmetry of the Hermite-Hadamard type inequalities is stressed by the different types of convexities. Several special cases of the parameter are chosen to illustrate the investigated results. Four examples are presented.

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