Abstract
In this paper, we introduce the class of extended s-(alpha,m)-preinvex functions. We establish a new fractional integral identity and derive some new fractional Hermite-Hadamard type inequalities for functions whose derivatives are in this novel class of function.
Highlights
It is well known that convexity plays an important and central role in many areas, such as economic, finance, optimization, and game theory
We introduce the class of extended s-(α, m)-preinvex functions
Motivated by the above results, in this paper, we introduce the class of extended s-(α, m)-preinvex functions
Summary
It is well known that convexity plays an important and central role in many areas, such as economic, finance, optimization, and game theory. Due to its diverse applications this concept has been extended and generalized in several directions. A where f is a real continuous convex function on the finite interval [a, b]. Zhu et al [12] established the following result connected with inequality (2). Motivated by the above results, in this paper, we introduce the class of extended s-(α, m)-preinvex functions. We establish a new fractional integral identity and derive some new fractional HermiteHadamard type inequalities for functions whose derivatives are in this novel class of functions. [19] A nonnegative function f : I ⊂ [0, ∞) → R is said to be s-convex in the second sense for some fixed s ∈ (0, 1], if f (tx + (1 − t)y) ≤ tsf (x) + (1 − t)sf (y) Definition 7. [19] A nonnegative function f : I ⊂ [0, ∞) → R is said to be s-convex in the second sense for some fixed s ∈ (0, 1], if f (tx + (1 − t)y) ≤ tsf (x) + (1 − t)sf (y)
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