Abstract
In this paper, we introduce and study the concept of exponential type P-function and establish Hermite-Hadamard's inequalities for this type of functions. In addition, we obtain some new Hermite-Hadamard type inequalities for functions whose first derivative in absolute value is exponential type P-function by using Hölder and power-mean integral inequalities. We also extend our initial results to functions of several variables. Next, we point out some applications of our results to give estimates for the approximation error of the integral the function in the trapezoidal formula and for some inequalities related to special means of real numbers.
Highlights
In this paper, we introduce and study the concept of exponential type P -function and establish Hermite-Hadamard’s inequalities for this type of functions
P -function which is connected with the concepts of P -function and exponential type convex function and establish some new Hermite-Hadamard type inequality for this class of functions
We introduce a new concept, which is called exponential type P -function and we give by setting some algebraic properties for the exponential type P -function, as follows: De...nition 6
Summary
R is an h-convex function, or that belongs to the class SX (h; I), if is non-negative and for all u; v 2 I; 2 (0; 1) we have ( r + (1 ) s) h( ) (r) + h(1 ) (s) : If this inequality is reversed, is said to be h-concave, i.e. 2 SV (h; I). If r < s and 2 L [r; s], the following Hermite-Hadamard type inequalities hold: p1 r+s. P -function which is connected with the concepts of P -function and exponential type convex function and establish some new Hermite-Hadamard type inequality for this class of functions. In recent years many authors have studied error estimations of Hermite-Hadamard type inequalities; for re...nements, counterparts, generalizations, for some related papers see [2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13]
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