The Journal of the Indian Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

A Note on Arc Lengths


Affiliations
1 Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, United States
2 Department of Applied Mathematics, National Chung-Hsing University, Taichung, 402, Taiwan, Province of China
3 Department of Mathematics, Central University, Chung-Li, 320, Taiwan, Province of China
     

   Subscribe/Renew Journal


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.
Subscription Login to verify subscription
User
Notifications
Font Size


  • 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.


Abstract Views: 362

PDF Views: 1




  • A Note on Arc Lengths

Abstract Views: 362  |  PDF Views: 1

Authors

Ravi P. Agarwal
Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, United States
Yuan-Chuan Li
Department of Applied Mathematics, National Chung-Hsing University, Taichung, 402, Taiwan, Province of China
Cheh-Chih Yeh
Department of Mathematics, Central University, Chung-Li, 320, Taiwan, Province of China

Abstract


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