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...
Main Authors: | , , , , , |
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Format: | Article |
Language: | English |
Published: |
SpringerOpen
2020-09-01
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Series: | Advances in Difference Equations |
Subjects: | |
Online Access: | http://link.springer.com/article/10.1186/s13662-020-02967-5 |
Summary: | 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. |
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ISSN: | 1687-1847 |