A refinement of Newton and Maclaurin inequalities through abstract convexity

TINAZTEPE G., Tinaztepe R.

TURKISH JOURNAL OF MATHEMATICS, vol.46, no.3, pp.699-709, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.3906/mat-2110-41
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.699-709
  • Keywords: Key words, Abstract convexity, Maclaurin inequality, Newton inequality
  • Akdeniz University Affiliated: Yes

Abstract

In this study, the refinements of Maclaurin's and Newton's inequalities are given. These refinements are obtained by applying the results on optimality conditions of abstract convex functions. When doing this, we obtain lower bounds for the solutions of some special rational equations.