- Open Mathematics Journal
- September 2022
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Inequalities play an important role in pure and applied mathematics. In particular, Jensen's inequality, one of the most famous inequalities, plays a main role in the study of the existence and uniqueness of initial and boundary value problems for differential equations.
In this work we prove some new Jensen-type inequalities for m-convex functions, and apply them to generalized Riemann-Liouville-type integral operators. Furthermore, as a remarkable consequence, some new inequalities for convex functions are obtained.
- jensen-type inequalities; convex functions; m-convex functions; fractional derivatives and integrals; fractional integral inequalitie