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Quantum Inequalities of Hermite–Hadamard Type for r -Convex Functions
Author(s) -
Xuexiao You,
Hasan Kara,
Hüseyin Budak,
Humaira Kalsoom
Publication year - 2021
Publication title -
journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.252
H-Index - 13
eISSN - 2314-4785
pISSN - 2314-4629
DOI - 10.1155/2021/6634614
Subject(s) - mathematics , convex function , type (biology) , hermite polynomials , hadamard transform , regular polygon , product (mathematics) , combinatorics , pure mathematics , mathematical analysis , geometry , ecology , biology
In this present study, we first establish Hermite–Hadamard type inequalities for r -convex functions via q κ 2 -definite integrals. Then, we prove some quantum inequalities of Hermite–Hadamard type for product of two r -convex functions. Finally, by using these established inequalities and the results given by (Brahim et al. 2015), we prove several quantum Hermite–Hadamard type inequalities for coordinated r -convex functions and for the product of two coordinated r -convex functions.

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