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, vol.7, no.8, 2023 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 8
  • Publication Date: 2023
  • Doi Number: 10.3390/fractalfract7080572
  • Journal Name: FRACTAL AND FRACTIONAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, Directory of Open Access Journals
  • Kocaeli University Affiliated: No

Abstract

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.