A new extension of quantum Simpson's and quantum Newton's type inequalities for quantum differentiable convex functions

Ali M. A., Budak H., Zhang Z.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, sa.4, ss.1845-1863, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1002/mma.7889
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1845-1863
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

In this paper, we prove two identities involving quantum derivatives, quantum integrals, and certain parameters. Using the newly proved identities, we prove new inequalities of Simpson's and Newton's type for quantum differentiable convex functions under certain assumptions. Moreover, we discuss the special cases of our main results and obtain some new and existing Simpson's type inequalities, Newton's type inequalities, midpoint type inequalities, and trapezoidal type inequalities.