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, vol.8, no.1, pp.1833-1847, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.3934/math.2023094
  • Journal Name: AIMS MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.1833-1847
  • Kocaeli University Affiliated: No

Abstract

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.