Affiliation:
1. Department of Mathematics, Faculty of Science and Arts Duzce University Duzce Türkiye
Abstract
The authors of the paper present a method to examine some Newton‐type inequalities for various function classes using Riemann‐Liouville fractional integrals. Namely, some fractional Newton‐type inequalities are established by using convex functions. In addition, several fractional Newton‐type inequalities are proved by using bounded functions by fractional integrals. Moreover, we construct some fractional Newton‐type inequalities for Lipschitzian functions. Furthermore, several Newton‐type inequalities are acquired by fractional integrals of bounded variation. Finally, we provide our results by using special cases of obtained theorems and examples.
Reference29 articles.
1. On new inequalities of Newton's type for functions whose second derivatives absolute values are convex;Gao S.;Int. J. Pure Appl. Math.,2012
2. Some Newton's type inequalities for harmonic convex functions;Noor M. A.;J. Adv. Math. Stud.,2016
3. Newton inequalities for p‐harmonic convex functions;Noor M. A.;Honam Math. J.,2018
4. Simpson- and Newton-Type Inequalities for Convex Functions via (p,q)-Calculus
5. A new extension of quantum Simpson's and quantum Newton's type inequalities for quantum differentiable convex functions