1. Jensen-type inequalities for m-convex functions
- Author
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Bosch, Paul, Quintana Mato, Yamilet del Carmen, Rodríguez García, José Manuel, Sigarreta Almira, José María, Comunidad de Madrid, Universidad Carlos III de Madrid, and Agencia Estatal de Investigación (España)
- Subjects
Convex functions ,Fractional derivatives and integrals ,Matemáticas ,General Mathematics ,M-convex functions ,Fractional integral inequalitie ,Jensen-type inequalities - Abstract
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. The research of Yamilet Quintana, José M. Rodríguez, and José M. Sigarreta is supported by a grant from Agencia Estatal de Investigación (PID2019-106433GB-I00/AEI/10.13039/501100011033), Spain. The research of Yamilet Quintana and José M. Rodríguez is supported by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23) and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation).
- Published
- 2022