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This paper introduced and investigated a new form of convex mapping known as $ \alpha $-exponential type convexity. We presented several algebraic properties associated with this newly introduced convexity. Additionally, we established novel adaptations of well-known inequalities, including the Hermite-Hadamard and Ostrowski-type inequalities, specifically for this convex function. We also derived special cases of these newly established results. Furthermore, we provided new estimations for the trapezoidal formula, demonstrating practical applications of this research.

This paper introduced and investigated a new form of convex mapping known as α-exponential type convexity. We presented several algebraic properties associated with this newly introduced convexity. Additionally, we established novel adaptations of well-known inequalities, including the Hermite-Hadamard and Ostrowski-type inequalities, specifically for this convex function. We also derived special cases of these newly established results. Furthermore, we provided new estimations for the trapezoidal formula, demonstrating practical applications of this research. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new Hermite-Hadamard type inequalities for differential exponential type convex functions and discuss several special cases. Moreover, in order to give the efficient of our main results, some applications for special means and error estimations are obtain.

Abstract In this manuscript, we give and study the concept of exponential type convex functions and some of their algebraic properties. We prove two Hermite–Hadamard (H-H) type integral inequalities for the newly introduced class of functions. We also obtain some refinements of the H-H inequality for functions whose first derivative in absolute value at certain power is exponential type convex.

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. [ABSTRACT FROM AUTHOR]

In this paper, the idea and its algebraic properties of n–polynomial exponential type p–convex function have been investigated. Authors prove new trapezium type inequality for this new class of functions. We also obtain some refinements of the trapezium type inequality for functions whose first derivative in absolute value at certain power are n–polynomial exponential type p–convex. At the end, some new bounds for special means of different positive real numbers are provided as well. These new results yield us some generalizations of the prior results. Our idea and technique may stimulate further research in different areas of pure and applied sciences.

In this manuscript, we give and study the concept of exponential type convex functions and some of their algebraic properties. We prove two Hermite–Hadamard (H-H) type integral inequalities for the newly introduced class of functions. We also obtain some refinements of the H-H inequality for functions whose first derivative in absolute value at certain power is exponential type convex. [ABSTRACT FROM AUTHOR]

In this paper, the idea and its algebraic properties of n -polynomial exponential type p -convex function have been investigated. Authors prove new trapezium type inequality for this new class of functions. We also obtain some refinements of the trapezium type inequality for functions whose first derivative in absolute value at certain power are n -polynomial exponential type p -convex. At the end, some new bounds for special means of different positive real numbers are provided as well. These new results yield us some generalizations of the prior results. Our idea and technique may stimulate further research in different areas of pure and applied sciences., Competing Interests: The authors declare no conflict of interest., (© 2020 Published by Elsevier Ltd.)