DSpace Arşivi :: by Yazar "Sitho, Surang" değerine göre listeleniyor

Listeleniyor 1 - 1 / 1

Trapezoid and Midpoint Type Inequalities for Preinvex Functions via Quantum Calculus
(Mdpi, 2021) Sitho, Surang; Ali, Muhammad Aamir; Budak, Hüseyin; Ntouyas, Sotiris K.; Tariboon, Jessada
In this article, we use quantum integrals to derive Hermite-Hadamard inequalities for preinvex functions and demonstrate their validity with mathematical examples. We use the q(x)(2)- quantum integral to show midpoint and trapezoidal inequalities for q(x)(2)-differentiable preinvex functions. Furthermore, we demonstrate with an example that the previously proved Hermite- Hadamard-type inequality for preinvex functions via q(x)(1)-quantum integral is not valid for preinvex functions, and we present its proper form. We use q(x)(1)-quantum integrals to show midpoint inequalities for q(x)(1)-differentiable preinvex functions. It is also demonstrated that by considering the limit q -> 1(-) and eta(x(2), x(1)) = -eta(x(1), x(2)) = x(2), x(1) in the newly derived results, the newly proved findings can be turned into certain known results.