Abstract
In this paper, we introduce and investigate a new class of generalized convex functions, known as generalized $r$-convex function. Some new Hermite-Hadamard integral inequalities via generalized $r$-convex functions have been established. Results proved in this paper can be viewed as significant new contributions in this area of research.
Highlights
In order to obtain some desirable results in general framework related to pure and applied sciences, the concept of convexity has been extended and generalized in several directions, see [1, 2, 4, 5, 7, 11,12,13,14,15,16,17]
We introduce and investigate a new class of generalized convex functions, known as generalized r-convex function
Hermite-Hadamard inequality is one of the most important inequality related to convex function, see [9, 10]
Summary
In order to obtain some desirable results in general framework related to pure and applied sciences, the concept of convexity has been extended and generalized in several directions, see [1, 2, 4, 5, 7, 11,12,13,14,15,16,17]. Much attention has been given to derive the Hermite-Hadamard type inequalities for various types of convex functions, see [8,9,10, 17, 18, 22]. Gill et al [8] introduced and investigated the concept of r-convex functions. They established some new Hermite-Hadamard integral inequalities for rconvex functions. Generalized convex functions; generalized r-convex functions; Hermite-Hadamard type inequalities. Inspired and motivated by the ongoing research, we introduce a new class of generalized convex functions, which is called generalized r-convex functions. We derive some new Hermite-Hadamard integral inequalities for these nonconvex functions.
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