Yazar "Ahmad, Hijaz" seçeneğine göre listele

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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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    A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable Operators
    (Hindawi Ltd, 2023) Kara, Hasan; Budak, Hueseyin; Etemad, Sina; Rezapour, Shahram; Ahmad, Hijaz; Kaabar, Mohammed K. A.
    This paper derives some equalities via twice differentiable functions and conformable fractional integrals. With the help of the obtained identities, we present new trapezoid-type and midpoint-type inequalities via convex functions in the context of the conformable fractional integrals. New inequalities are obtained by taking advantage of the convexity property, power mean inequality, and Holder's inequality. We show that this new family of inequalities generalizes some previous research studies by special choices. Furthermore, new other relevant results with trapezoid-type and midpoint-type inequalities are obtained.