Some Trapezium-Like Inequalities Involving Functions Having Strongly <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>n</mml:mi></mml:math>-Polynomial Preinvexity Property of Higher Order
Muhammad Uzair Awan, Sadia Talib, Muhammad Aslam Noor, Yu‐Ming Chu, Khalida Inayat Noor
Abstract
The main objective of this paper is to introduce a new class of preinvex functions which is called as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>n</mml:mi></mml:math>-polynomial preinvex functions of a higher order. As applications of this class of functions, we discuss several new variants of trapezium-like inequalities. In order to obtain the main results of the paper, we use the concepts and techniques of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mi>k</mml:mi></mml:math>-fractional calculus. We also discuss some special cases of the obtained results which show that the main results of the paper are quite unifying one.