New Estimates of the q-Hermite–Hadamard Inequalities via Strong Convexity

A refined version of the q-Hermite–Hadamard inequalities for strongly convex functions is introduced in this paper, utilizing both left and right q-integrals. Tighter bounds and more accurate estimates are derived by incorporating strong convexity. New q-trapezoidal and q-midpoint estimates are also...

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Bibliographic Details
Published in:Axioms Vol. 14; no. 8; p. 576
Main Authors: Sahatsathatsana, Chanokgan, Yotkaew, Pongsakorn
Format: Journal Article
Language:English
Published: Basel MDPI AG 25.07.2025
Subjects:
Calculus
Convex analysis
Convex functions
Convexity
Estimates
H-H type inequalities
Inequalities
Inequalities (Mathematics)
Integrals
Optimization
quantum calculus
strongly convex functions
Thailand
ISSN:2075-1680, 2075-1680
Online Access:Get full text
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Summary:A refined version of the q-Hermite–Hadamard inequalities for strongly convex functions is introduced in this paper, utilizing both left and right q-integrals. Tighter bounds and more accurate estimates are derived by incorporating strong convexity. New q-trapezoidal and q-midpoint estimates are also presented to enhance the precision of the results. The improvements in the results compared to previous work are demonstrated through numerical examples in terms of precision and tighter bounds, and the advantages of using strongly convex functions are showcased.
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content type line 14
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms14080576