Hermite-Hadamard-Type Integral Inequalities for Perspective Function

Silvestru Sever Dragomir ()
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Silvestru Sever Dragomir: Victoria University

A chapter in Approximation and Computation in Science and Engineering, 2022, pp 253-271 from Springer

Abstract: Abstract Let f : 0 , ∞ → ℝ $$f:\left ( 0,\infty \right ) \rightarrow \mathbb {R}$$ be a convex function on 0 , ∞ $$\left ( 0,\infty \right ) $$ . The associated two variables perspective function P f : 0 , ∞ × 0 , ∞ → ℝ $$P_{f}:\left ( 0,\infty \right ) \times \left ( 0,\infty \right ) \rightarrow \mathbb {R}$$ is defined by P f x , y : = x f y x . $$\displaystyle P_{f}\left ( x,y\right ) :=xf\left ( \frac {y}{x}\right ) . $$ In this paper, we establish some basic and double integral inequalities for the perspective function Pf defined above. Some double integral inequalities in the case of rectangles, squares, and circular sectors are also given.

Keywords: Convex functions; Perspective function; Hermite-Hadamard inequality; Double integral inequalities; 26D15 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-84122-5_14

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DOI: 10.1007/978-3-030-84122-5_14

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