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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
An, P.T. (2006): Stability of generalized monotone maps with respect to their characterizations. Optimization, 55, pp. 289-299
. An, P.T. (2006): A new kind of stable generalized convex functions. Journal of Inequalities in Pure and Applied Mathematics, 127(3), electronic
An, P.T. and Binh, V.T.T.: Stability of excess demand functions with respect to a strong version of Wald’s axiom. In Workshop “Small open economies in a globalised world”, Rimini, Italy, 29.8-2.9.2006, submitted for publication
Brighi, L. (2004): A strong criterion for the Weak Weak Axiom. Journal of Mathematical Economics, 40, pp. 93-103
Debreu, G. (1959): Theory of Value. Yale University Press, New Haven and London
Hildenbrand, W. and Jerison, M. (1989): The demand theory of the weak axioms of revealed preference. Economics Letters, 29, pp. 209-213
Houthakker, H.S. (1953): Revealed preference and the utility function. Economica, 17, pp. 159-174
Karamardian, S. and Schaible, S. (1990): Seven kinds of generalized monotone maps. Journal of Optimization Theory and Applications, 66, pp. 37-46
Karamardian, S. Schaible, S. and Crouzeix, J.P. (1993): Characterizations geneenralized monotone maps. Journal of Optimization Theory and Applications, 76, pp. 399-413
Kinderlehrer, D. and Stampacchia, G. (1980): An Introduction to Variational Inequalities and Their Applications. Academic, New York
John, R. (1998): Variational inequalities and pseudomonotone functions: some characterizations. In: Crouzeix, J.-P. et al. (ed) Generalized Convexity, Generalized Monotonicity. Kluwer, Dordrecht Boston London, 291-301
Mossin, A. (1972): A mean demand function and individual demand functions confronted with the weak and the strong axioms of revealed preference: an empirical test. Economica, 40, pp. 177-192
Ponstein, J. (1967): Seven kinds of convexity. SIAM Review, 9, pp. 115-119
Phu, H.X. and An, P.T. (1996): Stable generalization of convex functions. Optimization, 38, pp. 309-318
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
An, P.T. (2008). Stability of Generalized Convexity and Monotonicity. In: Konaté, D. (eds) Mathematical Modeling, Simulation, Visualization and e-Learning. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74339-2_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-74339-2_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74338-5
Online ISBN: 978-3-540-74339-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)