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Zeitschrift für Analysis und ihre Anwendungen


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Volume 24, Issue 2, 2005, pp. 389–400
DOI: 10.4171/ZAA/1247

Published online: 2005-06-30

Integral Inequalities in Higher Dimensional Spaces

SHIOJENN TSENG[1], PEN-CHI WANG[2], WING-SUM CHEUNG[3] and Chur-Jen Chen[4]

(1) Tamkang University, Taipei, Taiwan
(2) Tamkang University, Taipei, Taiwan
(3) University of Hong Kong, China
(4) Tunghai University, Taipei, Taiwan

Integral inequalities play an important role in many different areas including differential equations, integral equations, variational calculus, etc. In this work, we present some new higher dimensional integral inequalities involving monotonic or convex functions in higher dimensional spaces. These are then applied to solve directly some Calculus of Variations problems for optimal solutions, effectively.

Keywords: Integral inequalities, calculus of variations

TSENG SHIOJENN, WANG PEN-CHI, CHEUNG WING-SUM, Chen Chur-Jen: Integral Inequalities in Higher Dimensional Spaces. Z. Anal. Anwend. 24 (2005), 389-400. doi: 10.4171/ZAA/1247