Abstract
We analyze some properties of a recently introduced concept, the (α, λ)-concavity, useful to state a unified theory both in applications and optimization problems.
Two structural properties, monotonicity and concavifiability, are studied; but what is more interesting, once and twice differentiate (α, λ)-concave functions are characterized in order to find a continuous link between concavity and quasiconcavity.
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References
Ben-Tal A., On generalized Means and Generalized Concave Functions. J.O.T.A. (1977), vol. 21, pp. 1–13.
Castagnoli E. and Mazzoleni P., Towards a unified type of concavity. J.I.O.S. (1989a) vol.10, n. 1, pp.225–240.
Castagnoli E. and Mazzoleni P., About Derivatives of some Generalized Concave Functions. J.I.O.S, (1989b) vol.10, n. 1, pp.53–64.
Couzeix J.P., On second Order Conditions for Ouasiconvexitv. Math. Prog. (1980), vol.18, pp.349–352.
Crouzeix J.P. and Ferland J.A., Criteria for Ouasiconvexitv and Pseudoconvexity: Relationships and Comparisons. Math. Prog. (1982), vol.23, pp. 193–205.
Crouzeix J.P. and Lindberg. Additivelv Decomposed Ouasiconvex Functions. Math.Progr. (1986), pp.42–57.
Diewert W.E., Avriel M., and Zang I., Nine Kind of Quasiconcavity and Concavity. J.E.T. (1981), pp. 397–420.
Martos B., Nonlinear Programming; Theory and Methods, North Holland (1975).
Mereau P. and Paquet J., Second Order Conditions for Pseudoconvex Functions. SIAM J. of Appl. Math. (1974), vol.27 n. 1, pp.131–137.
Ortega J.M. and Rheinboldt W.C., Iterative Solution of Nonlinear Equations in Several Variables. (1970), Academic Press, New York.
Schaible S. and Ziemba W.T., (eds.), Generalized Concavity in Optimization and Economics. Academic Press, New York. (1981).
Zang I., Concavifiabilitv of C2 -functions: An Unified Approach. in Schaible and Ziemba (eds.)(1981), pp.131–152.
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© 1990 Springer-Verlag Berlin Heidelberg
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Castagnoli, E., Mazzoleni, P. (1990). Differentiable (α, λ) - Concave Functions. In: Cambini, A., Castagnoli, E., Martein, L., Mazzoleni, P., Schaible, S. (eds) Generalized Convexity and Fractional Programming with Economic Applications. Lecture Notes in Economics and Mathematical Systems, vol 345. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46709-7_5
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DOI: https://doi.org/10.1007/978-3-642-46709-7_5
Publisher Name: Springer, Berlin, Heidelberg
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