Some Generalizations of Different Types of Quantum Integral Inequalities for Differentiable Convex Functions with Applications

Zhao D., Ali M. A., Luangboon W., Budak H., Nonlaopon K.

FRACTAL AND FRACTIONAL, cilt.6, sa.3, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 6 Sayı: 3
  • Basım Tarihi: 2022
  • Doi Numarası: 10.3390/fractalfract6030129
  • Dergi Adı: FRACTAL AND FRACTIONAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus, INSPEC, Directory of Open Access Journals
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

In this paper, we prove a new quantum integral equality involving a parameter, left and right quantum derivatives. Then, we use the newly established equality and prove some new estimates of quantum Ostrowski, quantum midpoint, quantum trapezoidal and quantum Simpson's type inequalities for q-differentiable convex functions. It is also shown that the newly established inequalities are the refinements of the existing inequalities inside the literature. Finally, some examples and applications are given to illustrate the investigated results.