Trapezoidal-Type Inequalities for Strongly Convex and Quasi-Convex Functions via Post-Quantum Calculus.

Humaira Kalsoom,Miguel Vivas-Cortez,Muhammad Amer Latif

doi:10.3390/e23101238

Humaira Kalsoom, Miguel Vivas-Cortez + Show 1 more

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https://doi.org/10.3390/e23101238

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Abstract

In this paper, we establish new -integral and -integral identities. By employing these new identities, we establish new and - trapezoidal integral-type inequalities through strongly convex and quasi-convex functions. Finally, some examples are given to illustrate the investigated results.

Highlights

Introduction and PreliminariesQuantum calculus, often known as q-calculus, is a branch of mathematics that studies calculus without limits
Euler’s work on infinite series, which he integrated with Newton’s work on parameters, served as the idea for the q-calculus analysis, which was founded in the eighteenth century by famous mathematician Leonhard Euler (1707–1783)
I am a strong believer in this as it serves as a link between mathematics and physics, which is useful when working with physics

Summary

Introduction and Preliminaries

Often known as q-calculus, is a branch of mathematics that studies calculus without limits. In [21], Kunt et al proved the following Hermite–Hadamard-type inequalities for convex functions via (p, q)κ1 integral: Theorem 6 ([21]). If we suppose that all of the criteria of Lemma 5 are satisfied, the resulting inequality shows that κ2 Dp,qK σ is a strongly quasi-convex functions on [κ1, κ2] with modulus χ ≥ 1 for σ ≥ 1, κ2 dp,qx q(κ2 − κ1. The desired inequality (57) can be obtained by following the strategy applied in the proof of Theorem 9 and considering the Lemma 5

Examples

Conclusions