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V-Limit Analysis of Vector-Valued Mappings

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Ukrainian Mathematical Journal Aims and scope

Abstract

For an arbitrary net of mappings defined on subsets of the Hausdorff space (X, τ) and acting into a vector topological space (Y, τ) semiordered by a solid cone Λ, we introduce the notion of V-limit. We investigate topological and sequential properties of V-limit mappings and establish sufficient conditions for their existence. The results presented can be used as a basis for the procedure of averaging of problems of vector optimization.

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REFERENCES

  1. N. S. Bakhvalov and G. P. Panasenko, Averaging of Processes in Periodic Media[in Russian], Moscow, Nauka (1984).

    Google Scholar 

  2. V. V. Zhikov, S. M. Kozlov, and O. A. Oleinik, Averaging of Differential Operators[in Russian], Fizmatgiz, Moscow (1993).

    Google Scholar 

  3. P. I. Kogut, “S-convergence in the theory of averaging of problems of optimal control,” Ukr. Mat. Zh., 49, No.11, 1488–1498 (1997).

    Google Scholar 

  4. P. I. Kogut, “S-convergence in problems of conditional minimization and its variational properties,” Probl. Upravl. Informatiki, No. 4, 64–79 (1997).

    Google Scholar 

  5. P. I. Kogut, “On the Γ-representation of variational S-limits in problems of conditional minimization in normal Hausdorff spaces,” Kibern. Sistemn. Analiz, No. 1, 104–118 (1998).

    Google Scholar 

  6. E. G. Gol'shtein (editor), Methods for Optimization in Economical Mathematical Simulation[in Russian], Nauka, Moscow (1991).

    Google Scholar 

  7. A. G. Kusraev and S. S. Kutateladze, Subdifferential Calculus[in Russian], Nauka, Novosibirsk (1987).

    Google Scholar 

  8. V. V. Fedorchuk and V. V. Fillipov, General Topology. Basic Structures[in Russian], Moscow University, Moscow (1988).

    Google Scholar 

  9. M. Reed and B. Simon, Methods of Modern Mathematical Physics[Russian translation], Vol. 1, Mir, Moscow (1977).

    Google Scholar 

  10. G. Dal Maso, Introduction toΓ-Convergence, Birkhäuser, Boston (1993).

    Google Scholar 

  11. M. A. Krasnosel'skii, Positive Solutions of Operator Equations[in Russian], Fizmatgiz, Moscow (1962).

    Google Scholar 

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Authors and Affiliations

  1. Dnepropetrovsk Technical University of Railway Transport, Dnepropetrovsk

    P. I. Kogut

  2. Dnepropetrovsk Institute of Finances and Economics, Dnepropetrovsk

    T. M. Rudyanova

Authors
  1. P. I. Kogut
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  2. T. M. Rudyanova
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Kogut, P.I., Rudyanova, T.M. V-Limit Analysis of Vector-Valued Mappings. Ukrainian Mathematical Journal 52, 1896–1912 (2000). https://doi.org/10.1023/A:1010408010561

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