Abstract
The aim of this paper is to introduce a new class of preinvex functions which is called as generalized beta preinvex functions. We show that this class includes some other new classes of preinvex functions. We derive some new integral inequalities using the approach of quantum calculus. These integral inequalities involve generalized preinvex functions and q-Euler-Beta functions. Our results can be viewed as new quantum estimates for trapezoidal like inequalities. Some new special cases are also discussed which can be deduced from the main results of the paper.
Highlights
The property of convexity of a function has attracted several researchers over the years and this property has been generalized in different dimensions according to need, for some useful details, interested readers are referred to [3,4,6,9,14,15,17,18,24,25,28,34] and the references therein
In recent years several authors have investigated the class of h-convex functions with respect to integral inequalities
Ben Israel and Mond introduced the class of the invex sets and using invex sets as domain they defined the notion of preinvex functions
Summary
The property of convexity of a function has attracted several researchers over the years and this property has been generalized in different dimensions according to need, for some useful details, interested readers are referred to [3,4,6,9,14,15,17,18,24,25,28,34] and the references therein. Ben Israel and Mond introduced the class of the invex sets and using invex sets as domain they defined the notion of preinvex functions They have shown that the differentiable preinvex functions imply invex functions. Noor et al [25] extended the classes of preinvex functions and h-convex functions and introduced the notion of h-preinvex functions. It is expected that interested readers may find some novel applications of generalized preinvex functions and its related inequalities in other fields of pure and applied sciences. This is the main motivation of this paper
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