Author:
Ali Muhammad Aamir,Budak Hüseyin,Murtaza Ghulam,Chu Yu-Ming
Abstract
AbstractIn this research, we introduce the notions of $(p,q)$
(
p
,
q
)
-derivative and integral for interval-valued functions and discuss their fundamental properties. After that, we prove some new inequalities of Hermite–Hadamard type for interval-valued convex functions employing the newly defined integral and derivative. Moreover, we find the estimates for the newly proved inequalities of Hermite–Hadamard type. It is also shown that the results proved in this study are the generalization of some already proved research in the field of Hermite–Hadamard inequalities.
Funder
Natural Science Foundation of china
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference37 articles.
1. Ernst, T.: A Comprehensive Treatment of Q-calculus. Springer, Berlin (2012)
2. Ernst, T.: The History of Q-calculus and a New Method. Citeseer, Sweden (2000)
3. Gauchman, H.: Integral inequalities in q-calculus. Comput. Math. Appl. 47(2–3), 281–300 (2004)
4. Jackson, F.H.: On q-definite integrals. Q. J. Pure Appl. Math. 41, 193–203 (1910) Citeseer
5. Kac, V., Cheung, P.: Quantum Calculus. Springer, Berlin (2001)
Cited by
18 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