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Stability of Generalized Convexity and Monotonicity

In: Mathematical Modeling, Simulation, Visualization and e-Learning

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  • P. T. An

Abstract

It was shown that well-known kinds of generalized convex functions (generalized monotone maps, respectively) are often not stable with respect to the property they have to keep during the generalization. Then the so-called s-quasiconvex functions, s-quasimonotone maps and strictly s-quasiconvex functions were introduced in Optimization, vol.38, vol.55 and Journal of Inequalities in Pure and Applied Mathematics, vol.127, respectively. In this paper, some stability properties of such functions and a use of s-quasimonotonicity in an economics model are presented. Furthermore, an algorithm for finding the stability index for strict s-quasiconvexity of a given continuously twice differentiable function on ℝ is presented.

Suggested Citation

  • P. T. An, 2008. "Stability of Generalized Convexity and Monotonicity," Springer Books, in: Dialla Konaté (ed.), Mathematical Modeling, Simulation, Visualization and e-Learning, pages 193-200, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-74339-2_12
    DOI: 10.1007/978-3-540-74339-2_12
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