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

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  • Uğur Kadak
  • Yusuf Gürefe

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.

Suggested Citation

  • Uğur Kadak & Yusuf Gürefe, 2016. "A Generalization on Weighted Means and Convex Functions with respect to the Non-Newtonian Calculus," International Journal of Analysis, Hindawi, vol. 2016, pages 1-9, November.
    • Handle: RePEc:hin:ijanal:5416751
    DOI: 10.1155/2016/5416751
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    References listed on IDEAS

    as
    1. Uğur Kadak & Muharrem Özlük, 2015. "Generalized Runge-Kutta Method with respect to the Non-Newtonian Calculus," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-10, February.
    2. Ahmet Faruk Çakmak & Feyzi Başar, 2014. "Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, April.
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