About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 134751, 8 pages
http://dx.doi.org/10.1155/2013/134751
Research Article

Cone Monotonicity: Structure Theorem, Properties, and Comparisons to Other Notions of Monotonicity

Department of Mathematics, Washington State University, Pullman, WA 99164-3113, USA

Received 10 March 2013; Accepted 3 June 2013

Academic Editor: Pekka Koskela

Copyright © 2013 Heather A. Van Dyke et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Lebesgue, “Sur le problème de Dirichlet,” Rendiconti del Circolo Matematico di Palermo, vol. 27, pp. 371–402, 1907.
  2. G. D. Mostow, “Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms,” Institut des Hautes Études Scientifiques. Publications Mathématiques, no. 34, pp. 53–104, 1968. View at MathSciNet
  3. S. K. Vodopyanov and V. M. Goldstein, “Quasiconformal mappings and spaces of functions with generalized first derivatives,” Siberian Mathematical Journal, vol. 17, pp. 399–411, 1976.
  4. J. J. Manfredi, “Weakly monotone functions,” The Journal of Geometric Analysis, vol. 4, no. 3, pp. 393–402, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. S. G. Krantz and H. R. Parks, Geometric Integration Theory, Birkhäuser Boston Inc., Boston, Mass, USA, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, Fla, USA, 1992. View at Zentralblatt MATH · View at MathSciNet