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A Classroom Note on Twice Continuously Differentiable Strictly Convex and Strongly Quasiconvex Functions

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  • Giorgi Giorgio

Abstract

We provide some remarks and clarifications for twice continuously differentiable strictly convex and strongly quasiconvex functions. Characterizations of these classes and their relationships with other classes of generalized convex functions are also examined.

Suggested Citation

  • Giorgi Giorgio, 2018. "A Classroom Note on Twice Continuously Differentiable Strictly Convex and Strongly Quasiconvex Functions," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(3), pages 42-52, June.
    • Handle: RePEc:ibn:jmrjnl:v:10:y:2018:i:3:p:42
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    References listed on IDEAS

    as
    1. Murata, Yasuo, 1977. "Mathematics for Stability and Optimization of Economic Systems," Elsevier Monographs, Elsevier, edition 1, number 9780125112505 edited by Shell, Karl.
    2. Diewert, W. E. & Avriel, M. & Zang, I., 1981. "Nine kinds of quasiconcavity and concavity," Journal of Economic Theory, Elsevier, vol. 25(3), pages 397-420, December.
    3. Newman, Peter, 1969. "Some properties of concave functions," Journal of Economic Theory, Elsevier, vol. 1(3), pages 291-314, October.
    4. Vial, Jean-Philippe, 1982. "Strong convexity of sets and functions," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 187-205, January.
    5. Giorgio Giorgi, 2017. "Various Proofs of the Sylvester Criterion for Quadratic Forms," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(6), pages 55-66, December.
    6. Leroux, Alain, 1984. "Other determinental conditions for concavity and quasi-concavity," Journal of Mathematical Economics, Elsevier, vol. 13(1), pages 43-49, April.
    7. Otani, Kiyoshi, 1983. "A characterization of quasi-concave functions," Journal of Economic Theory, Elsevier, vol. 31(1), pages 194-196, October.
    8. VIAL, Jean-Philippe, 1982. "Strong convexity of sets and functions," LIDAM Reprints CORE 475, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Tyrrell Rockafellar, R., 1976. "Saddle points of Hamiltonian systems in convex Lagrange problems having a nonzero discount rate," Journal of Economic Theory, Elsevier, vol. 12(1), pages 71-113, February.
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    More about this item

    Keywords

    convexity; strict convexity; strong quasiconvexity; quasiconvexity; pseudoconvexity;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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