Implicit Function Theorems for Multi-Valued Mappings

  • B. N. Pshenichny
Part of the Ettore Majorana International Science Series book series (EMISS, volume 43)


Let us consider three Banach spaces X, Y, Z and operator F : X × YZ. We are interested in the solution of the following equation:
$$F\left( {x,y = 0} \right)$$


Banach Space Convex Cone Implicit Function Theorem Convex Analysis Finite Dimension 
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    B.N. Pshenichny. “Convex analysis and extremal problems”. Moscow, Nauka (1980), (in Russian).Google Scholar
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    T. Rockafellar. “Convex analysis.” Princeton Univ. Press, Princeton NJ (1970).zbMATHGoogle Scholar
  3. [3]
    B.G. Boltiansky. “The method of marquees in the theory of extremal problems”. Uspekhi matematichskih nauk vol. 3, No. 3 (1975), pp. 1–55 (in Russian).Google Scholar

Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

  • B. N. Pshenichny
    • 1
  1. 1.V.M. Glushkov Institut of CyberneticsKievUSSR

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