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    A Comprehensive Analysis of Hermite-Hadamard Type Inequalities via Generalized Preinvex Functions
    (Mdpi, 2021) Tariq, Muhammad; Ahmad, Hijaz; Budak, Hüseyin; Sahoo, Soubhagya Kumar; Sitthiwirattham, Thanin; Reunsumrit, Jiraporn
    The principal objective of this article is to introduce the idea of a new class of n-polynomial convex functions which we call n-polynomial s-type m-preinvex function. We establish a new variant of the well-known Hermite-Hadamard inequality in the mode of the newly introduced concept. To add more insight into the newly introduced concept, we have discussed some algebraic properties and examples as well. Besides, we discuss a few new exceptional cases for the derived results, which make us realize that the results of this paper are the speculations and expansions of some recently known outcomes. The immeasurable concepts and chasmic tools of this paper may invigorate and revitalize additional research in this mesmerizing and absorbing field.
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    Hermite-Hadamard-Mercer-Type Inequalities for Harmonically Convex Mappings
    (Mdpi, 2021) You, Xuexiao; Ali, Muhammad Aamir; Budak, Hüseyin; Reunsumrit, Jiraporn; Sitthiwirattham, Thanin
    In this paper, we prove Hermite-Hadamard-Mercer inequalities, which is a new version of the Hermite-Hadamard inequalities for harmonically convex functions. We also prove Hermite-Hadamard-Mercer-type inequalities for functions whose first derivatives in absolute value are harmonically convex. Finally, we discuss how special means can be used to address newly discovered inequalities.
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    On Some New Fractional Ostrowski- and Trapezoid-Type Inequalities for Functions of Bounded Variations with Two Variables
    (Mdpi, 2021) Sitthiwirattham, Thanin; Budak, Hüseyin; Kara, Hasan; Ali, Muhammad Aamir; Reunsumrit, Jiraporn
    In this paper, we first prove three identities for functions of bounded variations. Then, by using these equalities, we obtain several trapezoid- and Ostrowski-type inequalities via generalized fractional integrals for functions of bounded variations with two variables. Moreover, we present some results for Riemann-Liouville fractional integrals by special choice of the main results. Finally, we investigate the connections between our results and those in earlier works. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.