Browsing by Author "Abdul Mateen"

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    On some new simpsonÕs formula type inequalities for convex functions in post-quantum calculus
    (MDPI, 2021) Miguel J. Vivas-Cortez; Muhammad Aamir Ali; Shahid Qaisar; Ifra Bashir Sial; Sinchai Jansem; Abdul Mateen; M.J. Vivas-Cortez; Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Cat—lica del Ecuador, Escuela de Ciencias Matem‡ticas y F’sicas, Quito, Av. 12 de Octubre 1076, Apartado, 17-01-2184, Ecuador; email: mjvivas@puce.edu.ec; M.A. Ali; Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China; email: mahr.muhammad.aamir@gmail.com
    In this work, we prove a new (p, q)-integral identity involving a (p, q)-derivative and (p, q)-integral. The newly established identity is then used to show some new SimpsonÕs formula type inequalities for (p, q)-differentiable convex functions. Finally, the newly discovered results are shown to be refinements of comparable results in the literature. Analytic inequalities of this type, as well as the techniques used to solve them, have applications in a variety of fields where symmetry is important. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.