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, cilt.12, sa.7, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 7
  • Basım Tarihi: 2023
  • Doi Numarası: 10.3390/axioms12070691
  • Dergi Adı: AXIOMS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: convex functions, Bullen's inequality, Hadamard inequality, Holder inequality, power mean, fractional integral operators, HADAMARD, HERMITE
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.