Refine your search
Collections
Co-Authors
Year
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z All
Yeh, Cheh-Chih
- A Note on Arc Lengths
Abstract Views :303 |
PDF Views:1
Authors
Affiliations
1 Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, US
2 Department of Applied Mathematics, National Chung-Hsing University, Taichung, 402, TW
3 Department of Mathematics, Central University, Chung-Li, 320, TW
1 Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, US
2 Department of Applied Mathematics, National Chung-Hsing University, Taichung, 402, TW
3 Department of Mathematics, Central University, Chung-Li, 320, TW
Source
The Journal of the Indian Mathematical Society, Vol 83, No 1-2 (2016), Pagination: 1-11Abstract
The purpose of this paper is to give an analytic proof of an integral inequality due to Ozeki and Aoyaki. A simple application to the arc length of the parametric equation of a plane curve is also given.Keywords
Banach Space, Strictly Convex, Uniformly Convex, Arc Length, Bounded Variation, Rectifiable, Homeomorphism, Convex, Concave.References
- W. Arendt, C. J. K. Batty, M. Hieber and F. Neubrander, Vector-valued Laplaced Transforms and Cauchy Problems, Monographs in Mathematics, 96, 2001.
- Tom M. Apostol, Mathematical Analysis, Addison-Wesley Publishing Company, Inc. Addison-Wesley series in mathematics, 1975.
- J. Diestel and J. J. Uhl, Jr. Vector Measures, A.M.S. Math. Surveys, No. 15, 1977.
- K. Goebel and S. Reich, Uniform Convexity Hyperbolic Geometry, and Nonexpansive Mapping, Marcel Dekker Inc., New York and Basel, 1984.
- N. O. Ozeki and M. K. Aoyaki, Inequalities (in Japanese), 3rd. Maki Shoten, Tokyo, 1967.
- W. Rudin, Principles of Mathematic Analysis, New York, McGraw-Hill, 1976.
- W. Rudin, Real and Complex Analysis, New York, McGraw-Hill, 2nd Ed, 1984.
- S. Saks, Theory of the integral, Second revised edition. English translation by L. C. Young, Dover Publications, Inc., New York 1964.
- A. E. Taylor and D. C. Lay, Introduction to Functional Analysis, New York: Wiley 2nd Ed. 1980
- R. V'yborn'y, Kurzweil's Integral and Arc-length, Australian Math. Soc., Gazette, 8(1981), 19–22.