Some trapezoid and midpoint type inequalities for newly defined quantum integrals. (English) Zbl 1479.26020
Summary: In this paper, we first obtain prove two new identities for the quantum integrals. Then we establish Trapezoid and Midpoint type inequalities for quantum integrals defined by S. Bermudo et al. [Acta Math. Hung. 162, No. 1, 364–374 (2020; Zbl 1474.26085)]. The inequalities in this study generalize some results obtained in earlier works.
MSC:
| 26D15 | Inequalities for sums, series and integrals |
| 05A30 | \(q\)-calculus and related topics |
| 26A51 | Convexity of real functions in one variable, generalizations |
| 26E70 | Real analysis on time scales or measure chains |
| 33D15 | Basic hypergeometric functions in one variable, \({}_r\phi_s\) |
Keywords:
Hermite-Hadamard inequality; \(q\)-integral; quantum calculus; convex function; trapezoid; midpointCitations:
Zbl 1474.26085References:
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