Hermite–Hadamard-type inequalities via n-polynomial exponential-type convexity and their applications

Abstract

In this paper, we give and study the concept of n-polynomial $(s,m)$ ( s , m ) -exponential-type convex functions and some of their algebraic properties. We prove new generalization of Hermite–Hadamard-type inequality for the n-polynomial $(s,m)$ ( s , m ) -exponential-type convex function ψ. We also obtain some refinements of the Hermite–Hadamard inequality for functions whose first derivatives in absolute value at certain power are n-polynomial $(s,m)$ ( s , m ) -exponential-type convex. Some applications to special means and new error estimates for the trapezoid formula are given.

Hermite–Hadamard Type Inequalities via Generalized Harmonic Exponential Convexity and Applications

“…Awan et al [11] keeping his work on generalizations, introduced a new class called n-polynomial harmonically convex function. Motivated and inspired by the ongoing activities and research in the convex analysis field, we found out that there exists a special class of function known as exponential convex function, and nowadays, a lot of people working are in this field [12,13]. Dragomir [14] introduced the class of exponential type convexity.…”

Some Ostrowski Type Integral Inequalities using Hypergeometric Functions

“…Inequalities have an intriguing mathematical model because of its significant applications in traditional calculus, fractional calculus, quantum calculus, interval calculus, stochastic, time scale calculus, fractal sets, etc. For the applications, we encourage the readers to go through [5,6,7,8]. In such a manner, Ostrowski type inequality is quite possibly one of the most prominent contemplated results.…”

n–polynomial exponential type p–convex function with some related inequalities and their applications

“…It is also known as classical equation of (H–H) inequality. The Hermite–Hadamard inequality asserts that, if a function is convex in I for and , then Interested readers can refer to [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] .…”

“…Eventually the theory of inequalities may be regarded as an independent area of mathematics. For the applications of inequalities interested readers refer to [1,2,3,4,5,6]. In recent years, a wide class of integral inequalities is being derived via different concepts of convexity.…”

“…It is also known as classical equation of (H-H) inequality. The Hermite-Hadamard inequality asserts that, if a function ∶ ⊂ ℜ → ℜ is convex in for 1 , 2 ∈ and 1 < 2 , then Interested readers can refer to [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28].…”