On equivalent characterizations of convexity of functions

Authors

Eleftherios Gkioulekas, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

2013

Abstract

A detailed development of the theory of convex functions, not often found in complete form in most textbooks, is given. We adopt the strict secant line definition as the definitive definition of convexity. We then show that for differentiable functions, this definition becomes logically equivalent with the first derivative monotonicity definition and the tangent line definition. Consequently, for differentiable functions, all three characterizations are logically equivalent.

Comments

Original published version available at https://doi.org/10.1080/0020739X.2012.703336

Recommended Citation

Eleftherios Gkioulekas gkioulekase@utpa.edu (2013) On equivalent characterizations of convexity of functions, International Journal of Mathematical Education in Science and Technology, 44:3, 410-417, https://doi.org/10.1080/0020739X.2012.703336

Publication Title

International Journal of Mathematical Education in Science and Technology

DOI

10.1080/0020739X.2012.703336