Browsing by Author "Muhammad Amir Ashraf"

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    On New Estimates of q-HermiteÐHadamard Inequalities with Applications in Quantum Calculus
    (MDPI, 2023) Saowaluck Chasreechai; Muhammad Aamir Ali; Muhammad Amir Ashraf; Thanin Sitthiwirattham; Sina Etemad; Manuel De la Sen; Shahram Rezapour; S. Etemad; Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, 3751-71379, Iran; email: sina.etemad@azaruniv.ac.ir; S. Rezapour; Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, 3751-71379, Iran; email: sh.rezapour@azaruniv.ac.ir; M.D.L. Sen; Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country (UPV/EHU), Leioa, Bizkaia, 48940, Spain; email: manuel.delasen@ehu.eus
    In this paper, we first establish two quantum integral (q-integral) identities with the help of derivatives and integrals of the quantum types. Then, we prove some new q-midpoint and q-trapezoidal estimates for the newly established q-Hermite-Hadamard inequality (involving left and right integrals proved by Bermudo et al.) under q-differentiable convex functions. Finally, we provide some examples to illustrate the validity of newly obtained quantum inequalities. © 2023 by the authors.