Abstract
In the paper we propose very general definition of approximate midconvexity. Let α: [0, ∞) → ℝ be a given function. Let X be a normed space and V a convex subset of X. A function f: V → ℝ will be called α(⋅) - midconvex if
The above definition simultaneously generalizes approximate and uniform midconvexities. We present several results concerning this notion.
Keywords
Mathematics Subject Classification (2001): Primary 26A51, 26B25
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Misztal, K., Tabor, J., Tabor, J. (2011). Approximately Midconvex Functions. In: Rassias, T., Brzdek, J. (eds) Functional Equations in Mathematical Analysis. Springer Optimization and Its Applications(), vol 52. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0055-4_14
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DOI: https://doi.org/10.1007/978-1-4614-0055-4_14
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