Author:
Butt Saad Ihsan,Kashuri Artion,Tariq Muhammad,Nasir Jamshed,Aslam Adnan,Gao Wei
Abstract
AbstractIn 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.
Funder
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference22 articles.
1. Alomari, M., Darus, M., Kirmaci, U.S.: Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means. Comput. Math. Appl. 59, 225–232 (2010)
2. Chen, F.X., Wu, S.H.: Several complementary inequalities to inequalities of Hermite–Hadamard type for s-convex functions. J. Nonlinear Sci. Appl. 9(2), 705–716 (2016)
3. Dragomir, S.S., Fitzpatrik, S.: The Hadamard’s inequality for s-convex functions in the second sense. Demonstr. Math. 32(4), 687–696 (1999)
4. Eftekhari, N.: Some remarks on $(s,m)$-convexity in the second sense. J. Math. Inequal. 8, 489–495 (2014)
5. Hudzik, H., Maligranda, L.: Some remarks on s-convex functions. Aequ. Math. 48, 100–111 (1994)
Cited by
31 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献