Browsing by Author "Miguel J. Vivas-Cortez"

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    On Generalization of Different Integral Inequalities for Harmonically Convex Functions
    (MDPI, 2022) Jiraporn Reunsumrit; Miguel J. Vivas-Cortez; Muhammad Aamir Ali; Thanin Sitthiwirattham; M.J. Vivas-Cortez; Escuela de Ciencias Matem‡ticas y F’sicas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Cat—lica del Ecuador, Quito, Av. 12 de Octubre 1076, Apartado, 17-01-2184, Ecuador; email: mjvivas@puce.edu.ec
    In this study, we first prove a parameterized integral identity involving differentiable functions. Then, for differentiable harmonically convex functions, we use this result to establish some new inequalities of a midpoint type, trapezoidal type, and Simpson type. Analytic inequalities of this type, as well as the approaches for solving them, have applications in a variety of domains where symmetry is important. Finally, several particular cases of recently discovered results are discussed, as well as applications to the special means of real numbers. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
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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.