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New inequalities for $\eta$-quasiconvex functions
- Publication Year :
- 2018
-
Abstract
- The class of $\eta$-quasiconvex functions was introduced in 2016. Here we establish novel inequalities of Ostrowski type for functions whose second derivative, in absolute value raised to the power $q\geq 1$, is $\eta$-quasiconvex. Several interesting inequalities are deduced as special cases. Furthermore, we apply our results to the arithmetic, geometric, Harmonic, logarithmic, generalized log and identric means, getting new relations amongst them.<br />Comment: This is a preprint of a paper whose final and definite form is accepted 19-Sept-2018 as a book chapter at Springer New York, on the topic of 'Frontiers in Functional Equations and Analytic Inequalities', Edited by G. Anastassiou and J. Rassias
- Subjects :
- Mathematics - Classical Analysis and ODEs
26D15, 26E60, 26A51
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1809.07377
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/978-3-030-28950-8_22