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Volume 15
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10.3390/sym15081514
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Article

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

by
Loredana Ciurdariu
1,* and
Eugenia Grecu
2
1
Department of Mathematics, Politehnica University of Timisoara, 300006 Timisoara, Romania
2
Department of Management, Politehnica University of Timisoara, 300006 Timisoara, Romania
*
Author to whom correspondence should be addressed.
Symmetry 2023, 15(8), 1514; https://doi.org/10.3390/sym15081514
Submission received: 4 July 2023 / Revised: 26 July 2023 / Accepted: 27 July 2023 / Published: 31 July 2023
(This article belongs to the Special Issue Symmetry in Quantum Calculus)
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Abstract

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.
Keywords: q-calculus; convexity; midpoint inequalities; Hermite-Hadamard type inequalities q-calculus; convexity; midpoint inequalities; Hermite-Hadamard type inequalities

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MDPI and ACS Style

Ciurdariu, L.; Grecu, E. New Perspectives of Symmetry Conferred by q-Hermite-Hadamard Type Integral Inequalities. Symmetry 2023, 15, 1514. https://doi.org/10.3390/sym15081514

AMA Style

Ciurdariu L, Grecu E. New Perspectives of Symmetry Conferred by q-Hermite-Hadamard Type Integral Inequalities. Symmetry. 2023; 15(8):1514. https://doi.org/10.3390/sym15081514

Chicago/Turabian Style

Ciurdariu, Loredana, and Eugenia Grecu. 2023. "New Perspectives of Symmetry Conferred by q-Hermite-Hadamard Type Integral Inequalities" Symmetry 15, no. 8: 1514. https://doi.org/10.3390/sym15081514

APA Style

Ciurdariu, L., & Grecu, E. (2023). New Perspectives of Symmetry Conferred by q-Hermite-Hadamard Type Integral Inequalities. Symmetry, 15(8), 1514. https://doi.org/10.3390/sym15081514

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