Browsing by Subject "(p, q) -calculus"

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    A new version of (p, q) -HermiteÐHadamardÕs midpoint and trapezoidal inequalities via special operators in (p, q) -calculus
    (Springer Science and Business Media Deutschland GmbH, 2022) Thanin Sitthiwirattham; Muhammad Aamir Ali; HŸseyin Budak; Sina Etemad; Shahram Rezapour; S. Rezapour; Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran; email: sh.rezapour@azaruniv.ac.ir
    In this paper, we conduct a research on a new version of the (p, q) -HermiteÐHadamard inequality for convex functions in the framework of postquantum calculus. Moreover, we derive several estimates for (p, q) -midpoint and (p, q) -trapezoidal inequalities for special (p, q) -differentiable functions by using the notions of left and right (p, q) -derivatives. Our newly obtained inequalities are extensions of some existing inequalities in other studies. Lastly, we consider some mathematical examples for some (p, q) -functions to confirm the correctness of newly established results. © 2022, The Author(s).
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    On fractional (p, q) -calculus
    (Springer, 2020) Jarunee Soontharanon; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, Thailand; email: thanin_sit@dusit.ac.th
    In this paper, the new concepts of (p, q) -difference operators are introduced. The properties of fractional (p, q) -calculus in the sense of a (p, q) -difference operator are introduced and developed. © 2020, The Author(s).