Sharp trapezoid and mid-point type inequalities on closed balls in R3

This paper deals with some trapezoid and mid-point type inequalities on closed balls in R 3 . Three kinds of functions are considered: convex, Lipschitz, and bounded functions. The spherical coordinates are used to obtain sharp inequalities. Also a reverse result is given for the right-hand side of...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2020; no. 1
Main Author Rostamian, Delavar M
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2020
Springer Nature B.V
Subjects
Analysis
Applications of Mathematics
Closed balls
Inequalities
Mathematics
Mathematics and Statistics
Spherical coordinates
26A51
Trapezoid type inequality
Mid-point type inequality
26B15
Hermite–Hadamard inequality
26B25
Spherical coordinates
26D15
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Summary:This paper deals with some trapezoid and mid-point type inequalities on closed balls in R 3 . Three kinds of functions are considered: convex, Lipschitz, and bounded functions. The spherical coordinates are used to obtain sharp inequalities. Also a reverse result is given for the right-hand side of Hermite–Hadamard’s inequality obtained on closed balls in R 3 .
ISSN:1025-5834
1029-242X
DOI:10.1186/s13660-020-02377-x