Title: Quantum Integral Inequalities Via Different Variants of Parameterized Harmonically Convex Functions on Finite Intervals With Related Applications.
Authors: Shah, Ahsan Fareed; Boulaaras, Salah Mahmoud; Wong, Patricia J. Y.; Saleem, Muhammad Shoaib; Umair Shahzad, Muhammad
Abstract: This work introduces a new concept, k$$ k $$‐harmonically γ$$ \gamma $$‐convex function, which covers some important variants of harmonically convex functions previously presented in the literature. We have established well‐known Hermite‐Hadamard–type integral inequalities for this newly defined convexity using generalized quantum integrals. In addition, we discussed this well‐known inequality on finite intervals using quantum integrals. Finally, we validated our unique findings using some examples, such as Python‐programmed graphs and Mathematica.
Subjects: FRACTIONAL calculus; GENERALIZED integrals; CONVEX functions; INTEGRAL functions; INTEGRALS; INTEGRAL inequalities
Publication: Mathematical Methods in the Applied Sciences, 2025, Vol 48, Issue 8, p9194
ISSN: 0170-4214
Publication type: Academic Journal
DOI: 10.1002/mma.10792

Quantum Integral Inequalities Via Different Variants of Parameterized Harmonically Convex Functions on Finite Intervals With Related Applications.

Shah, Ahsan Fareed; Boulaaras, Salah Mahmoud; Wong, Patricia J. Y.; Saleem, Muhammad Shoaib; Umair Shahzad, Muhammad