The Idzik type quasivariational inequalities and noncompact optimization problems

Sehie Park; Jong Park

Colloquium Mathematicae (1996)

  • Volume: 71, Issue: 2, page 287-295
  • ISSN: 0010-1354

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Park, Sehie, and Park, Jong. "The Idzik type quasivariational inequalities and noncompact optimization problems." Colloquium Mathematicae 71.2 (1996): 287-295. <http://eudml.org/doc/210442>.

@article{Park1996,
author = {Park, Sehie, Park, Jong},
journal = {Colloquium Mathematicae},
keywords = {topological vector space (t.v.s.); compact map; measure of noncompactness; convexly totally bounded (c.t.b.); closed map; quasivariational inequality; multifunction (map); 𝛷-condensing map; fixed point theorem; quasivariational inequalities; condensing maps; noncompact optimization problems},
language = {eng},
number = {2},
pages = {287-295},
title = {The Idzik type quasivariational inequalities and noncompact optimization problems},
url = {http://eudml.org/doc/210442},
volume = {71},
year = {1996},
}

TY - JOUR
AU - Park, Sehie
AU - Park, Jong
TI - The Idzik type quasivariational inequalities and noncompact optimization problems
JO - Colloquium Mathematicae
PY - 1996
VL - 71
IS - 2
SP - 287
EP - 295
LA - eng
KW - topological vector space (t.v.s.); compact map; measure of noncompactness; convexly totally bounded (c.t.b.); closed map; quasivariational inequality; multifunction (map); 𝛷-condensing map; fixed point theorem; quasivariational inequalities; condensing maps; noncompact optimization problems
UR - http://eudml.org/doc/210442
ER -

References

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  1. [BP] A. Behera and G. K. Panda, A generalization of Browder's theorem, Bull. Inst. Math. Acad. Sinica 21 (1993), 183-186. Zbl0780.90098
  2. [B] C. Berge, Espaces Topologiques, Dunod, Paris, 1959. 
  3. [B1] F. E. Browder, A new generalization of the Schauder fixed point theorem, Math. Ann. 174 (1967), 285-290. Zbl0176.45203
  4. [B2] F. E. Browder, The fixed point theory of multi-valued mappings in topological vector spaces, ibid. 177 (1968), 283-301. 
  5. [F] K. Fan, Fixed-point and minimax theorems in locally convex topological linear spaces, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 121-126. Zbl0047.35103
  6. [H] O. Hadžić, Fixed point theory in topological vector spaces, Univ. of Novi Sad, Novi Sad, 1984. Zbl0576.47030
  7. [HS] P. Hartman and G. Stampacchia, On some nonlinear elliptic differential equations, Acta Math. 115 (1966), 271-310. Zbl0142.38102
  8. [I1] A. Idzik, Remarks on Himmelberg's fixed point theorems, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), 909-912. Zbl0403.47025
  9. [I2] A. Idzik, Fixed point theorems for families of functions, ibid., 913-916. Zbl0403.47029
  10. [I3] A. Idzik, Almost fixed point theorems, Proc. Amer. Math. Soc. 104 (1988), 779-784. Zbl0691.47046
  11. [IK] S. M. Im and W. K. Kim, An application of Himmelberg's fixed point theorem to non-compact optimization problems, Bull. Inst. Math. Acad. Sinica 19 (1991), 1-5. Zbl0754.47037
  12. [JK] R. K. Juberg and S. Karamardian, On variational type inequalities, Boll. Un. Mat. Ital. (4) 7 (1973), 336-338. Zbl0269.49019
  13. [KZ] T. Kaczyński and V. Zeidan, An application of Ky Fan fixed point theorem to an optimization problem, Nonlinear Anal. 13 (1989), 259-261. Zbl0685.49009
  14. [K] S. Karamardian, Generalized complementarity problem, J. Optim. Theory Appl. 8 (1971), 161-168. Zbl0218.90052
  15. [LS] J. L. Lions and G. Stampacchia, Variational inequalities, Comm. Pure Appl. Math. 20 (1967), 493-519. Zbl0152.34601
  16. [M] T.-W. Ma, On sets with convex sections, J. Math. Anal. Appl. 27 (1969), 413-416. Zbl0176.42703
  17. [MTY] G. B. Mehta, K.-K. Tan and X.-Z. Yuan, Maximal elements and generalized games in locally convex topological vector spaces, Bull. Polish Acad. Sci. Math. 42 (1994), 43-53. 
  18. [Mo] U. Mosco, Implicit variational problems and quasi variational inequalities, in: Nonlinear Operators and the Calculus of Variations, Lecture Notes in Math. 543, Springer, 1976, 83-156. 
  19. [N] J. Nash, Non-cooperative games, Ann. of Math. 54 (1951), 286-293. Zbl0045.08202
  20. [PSK] J. Parida, M. Sahoo and A. Kumar, A variational-like inequality problem, Bull. Austral. Math. Soc. 39 (1989), 225-231. Zbl0649.49007
  21. [P1] S. Park, Remarks on some variational inequalities, Bull. Korean Math. Soc. 28 (1991), 163-174. Zbl0753.47035
  22. [P2] S. Park, Some existence theorems for two variable functions on topological vector spaces, Kangweon-Kyungki Math. J. 3 (1995), 11-16. 
  23. [PC] S. Park and M.-P. Chen, Generalized quasi-variational inequalities, Far East J. Math. Sci. 3 (1995), 199-204. 
  24. [PF] W. V. Petryshyn and P. M. Fitzpatrick, Fixed-point theorems for multivalued noncompact inward maps, J. Math. Anal. Appl. 46 (1974), 756-767. Zbl0287.47038
  25. [SKA] A. H. Siddiqi, A. Khaliq and Q. H. Ansari, On variational-like inequalities, Ann. Sci. Math. Québec 18 (1994), 95-104. Zbl0807.47054
  26. [S] G. Stampacchia, Variational inequalities, in: Theory and Application of Monotone Operators, A. Ghizzetti (ed.), Edizioni Oderisi, Gubbio, 1969, 101-192. 
  27. [T] W. Takahashi, Existence theorems generalizing fixed point theorems for multivalued mappings, in: Fixed Point Theory and Applications, M. A. Théra and J.-B. Baillon (eds.), Longman Sci. & Tech., Essex, 1991, 397-406. Zbl0760.47029
  28. [W] H. Weber, Compact convex sets in non-locally convex linear spaces, Schauder-Tychonoff fixed point theorem, in: Topology, Measures, and Fractals (Warnemünde, 1991), Math. Res. 66, Akademie-Verlag, Berlin, 1992, 37-40. Zbl0760.47030

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