Some q-analogues of Hermite–Hadamard inequality of functions of two variables on finite rectangles in the plane

M. A. Latif; S. S. Dragomir; E. Momoniat

doi:10.1016/j.jksus.2016.07.001

Some q-analogues of Hermite–Hadamard inequality of functions of two variables on finite rectangles in the plane

M. A. Latif, S. S. Dragomir, E. Momoniat

Research output: Contribution to journal › Article › peer-review

43 Citations (Scopus)

Abstract

Preliminaries of q-calculus for functions of two variables over finite rectangles in the plane are introduced. Some q-analogues of the famous Hermite–Hadamard inequality of functions of two variables defined on finite rectangles in the plane are presented. A q₁q₂-Hölder inequality for functions of two variables over finite rectangles is also established to provide some quantum estimates of trapezoidal type inequality of functions of two variables whose q₁q₂-partial derivatives in absolute value with certain powers satisfy the criteria of convexity on co-ordinates.

Original language	English
Pages (from-to)	263-273
Number of pages	11
Journal	Journal of King Saud University - Science
Volume	29
Issue number	3
DOIs	https://doi.org/10.1016/j.jksus.2016.07.001
Publication status	Published - Jul 2017
Externally published	Yes

Keywords

Hermite–Hadamard inequality
Quantum calculus
qq-Hölder inequality
qq-Partial derivatives

ASJC Scopus subject areas

Multidisciplinary

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10.1016/j.jksus.2016.07.001

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abstract = "Preliminaries of q-calculus for functions of two variables over finite rectangles in the plane are introduced. Some q-analogues of the famous Hermite–Hadamard inequality of functions of two variables defined on finite rectangles in the plane are presented. A q1q2-H{\"o}lder inequality for functions of two variables over finite rectangles is also established to provide some quantum estimates of trapezoidal type inequality of functions of two variables whose q1q2-partial derivatives in absolute value with certain powers satisfy the criteria of convexity on co-ordinates.",

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AU - Momoniat, E.

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AB - Preliminaries of q-calculus for functions of two variables over finite rectangles in the plane are introduced. Some q-analogues of the famous Hermite–Hadamard inequality of functions of two variables defined on finite rectangles in the plane are presented. A q1q2-Hölder inequality for functions of two variables over finite rectangles is also established to provide some quantum estimates of trapezoidal type inequality of functions of two variables whose q1q2-partial derivatives in absolute value with certain powers satisfy the criteria of convexity on co-ordinates.

KW - Hermite–Hadamard inequality

KW - Quantum calculus

KW - qq-Hölder inequality

KW - qq-Partial derivatives

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ER -

Some q-analogues of Hermite–Hadamard inequality of functions of two variables on finite rectangles in the plane

Abstract

Keywords

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