On Some New Maclaurin's Type Inequalities for Convex Functions in <i>q</i>-Calculus

Sitthiwirattham T., Ali M. A., Budak H.

FRACTAL AND FRACTIONAL, cilt.7, sa.8, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 7 Sayı: 8
  • Basım Tarihi: 2023
  • Doi Numarası: 10.3390/fractalfract7080572
  • Dergi Adı: FRACTAL AND FRACTIONAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, Directory of Open Access Journals
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

This work establishes some new inequalities to find error bounds for Maclaurin's formulas in the framework of q-calculus. For this, we first prove an integral identity involving q-integral and q-derivative. Then, we use this new identity to prove some q-integral inequalities for q-differentiable convex functions. The inequalities proved here are very important in the literature because, with their help, we can find error bounds for Maclaurin's formula in both q and classical calculus.