Some New Bullen-Type Inequalities Obtained via Fractional Integral Operators

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Fahad A., Butt S. I., BAYRAKTAR B., Anwar M., Wang Y.

AXIOMS, vol.12, no.7, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 7
  • Publication Date: 2023
  • Doi Number: 10.3390/axioms12070691
  • Journal Name: AXIOMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: convex functions, Bullen's inequality, Hadamard inequality, Holder inequality, power mean, fractional integral operators, HADAMARD, HERMITE
  • Bursa Uludag University Affiliated: Yes

Abstract

In this paper, we establish a new auxiliary identity of the Bullen type for twice-differentiable functions in terms of fractional integral operators. Based on this new identity, some generalized Bullen-type inequalities are obtained by employing convexity properties. Concrete examples are given to illustrate the results, and the correctness is confirmed by graphical analysis. An analysis is provided on the estimations of bounds. According to calculations, improved Holder and power mean inequalities give better upper-bound results than classical inequalities. Lastly, some applications to quadrature rules, modified Bessel functions and digamma functions are provided as well.