On generalizations of trapezoid and Bullen type inequalities based on generalized fractional integrals

Budak H., Ertugral F., Ali M. A., Bilisik C. C., Sarikaya M. Z., Nonlaopon K.

AIMS MATHEMATICS, cilt.8, sa.1, ss.1833-1847, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 8 Sayı: 1
  • Basım Tarihi: 2023
  • Doi Numarası: 10.3934/math.2023094
  • Dergi Adı: AIMS MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.1833-1847
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

In this paper, we establish an integral identity involving differentiable functions and generalized fractional integrals. Then, using the newly established identity, we prove some new general versions of Bullen and trapezoidal type inequalities for differentiable convex functions. The main benefit of the newly established inequalities is that they can be converted into similar inequalities for classical integrals, Riemann-Liouville fractional integrals, k-Riemann-Liouville fractional integrals, Hadamard fractional integrals, etc. Moreover, the inequalities presented in the paper are extensions of several existing inequalities in the literature.