Advertisement

Journal of Optimization Theory and Applications

, Volume 41, Issue 2, pp 377–387 | Cite as

Elementary properties of arcwise connected sets and functions

  • C. Singh
Technical Note

Abstract

The purpose of this paper is to investigate some elementary, basic properties of arcwise connected sets and functions. Since these concepts are generalizations of convexity, it is natural to ask if any of the basic properties of convex sets and functions are carried over to these new generalized classes. All the functions involved are considered to be not necessarily differentiable.

Key Words

Convexity arcwise connectedness continuity locally bounded functions Lipschitz condition epigraph 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ortega, J. M., andRheinboldt, W. C.,Iterative Solutions of Nonlinear Equations in Several Variables, Academic Press, New York, New York, 1970.Google Scholar
  2. 2.
    Avriel, M., andZang, I.,Generalized Arcwise-Connected Functions and Characterization of Local-Global Minimum Properties, Journal of Optimization Theory and Applications, Vol. 32, pp. 407–425, 1980.Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • C. Singh
    • 1
  1. 1.St. Lawrence UniversityCanton

Personalised recommendations