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New Applications of γ-Quasiconvexity

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Applications of Nonlinear Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 134))

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Abstract

This survey deals with inequalities satisfied by γ-quasiconvex functions which are one of the many variants of convex functions. The γ-quasiconvex functions have already been dealt with by S. Abramovich, L.-E. Persson and N. Samko. Among the applications we demonstrate here are Jensen, Hardy, Hölder, Minkowski, Jensen-Steffensen and Slater-Pečarić inequalities. These inequalities can be seen as extensions and refinements of inequalities satisfied by convex functions.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Haifa, Haifa, Israel

    Shoshana Abramovich

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  1. Shoshana Abramovich
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Correspondence to Shoshana Abramovich .

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Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Abramovich, S. (2018). New Applications of γ-Quasiconvexity. In: Rassias, T. (eds) Applications of Nonlinear Analysis . Springer Optimization and Its Applications, vol 134. Springer, Cham. https://doi.org/10.1007/978-3-319-89815-5_1

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