A Generalization on Weighted Means and Convex Functions with respect to the Non-Newtonian Calculus


Kadak U., GÜREFE Y.

INTERNATIONAL JOURNAL OF ANALYSIS, 2016 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2016
  • Doi Number: 10.1155/2016/5416751
  • Title of Journal : INTERNATIONAL JOURNAL OF ANALYSIS

Abstract

This paper is devoted to investigating some characteristic features of weighted means and convex functions in terms of the non-Newtonian calculus which is a self-contained system independent of any other system of calculus. It is shown that there are infinitely many such useful types of weighted means and convex functions depending on the choice of generating functions. Moreover, some relations between classical weighted mean and its non-Newtonian version are compared and discussed in a table. Also, some geometric interpretations of convex functions are presented with respect to the non-Newtonian slope. Finally, using multiplicative continuous convex functions we give an application.