Some Generalizations of Mulit-Valued Version of Schauder’s Fixed Point Theorem with Applications

• BAPURAO C DHAGE ^[1]
  1. [1] Gurukul Colony Kasubai
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 12, Nº. 3, 2010, págs. 139-151
• Idioma: inglés
• DOI: 10.4067/S0719-06462010000300009
• Enlaces
  • Texto completo
• Resumen
  • español

    En este artículo probamos una generalización para el teorema del punto fijo de Kakutani- Fan para aplicaciones multi-valuadas en espacios de Banach, bajo condición de semi-continuidad superior debil. Este resultado es aplicado para obtener una versión generalizada del teorema del punto fijo Krasnoselskii y algunas alternativas de tipo Leray-Schauder para aplicaciones multi-valuadas cerradas en espacios de Banach.

  • English

    In this article, a generalization of a Kakutani-Fan fixed point theorem for multi-valued mappings in Banach spaces is proved under weaker upper semi-continuity condition and it is further applied to derive a generalized version of Krasnoselskii’s fixed point theorem and some nonlinear alternatives of Leray-Schauder type for multi-valued closed mappings in Banach spaces.

• Referencias bibliográficas
  • AGARWAL, R.P,MEEHAN, M,O’REGAN, D. (2001). Fixed Point Theory and Applications. Cambridge Univ. Press.
  • AKHMEROV, R.R,KAMENSKII, M.I,POTAPOV, A.S,RODHINA, A.E,SADOVSKII, B.N. (1992). Measures of Noncompactness and Condensing Operators. Birkhauser...
  • BANAS, J,GOEBEL, K. (1980). Measures of Noncompactness in Banach Spaces: LNPAM. Marcel Dekker. ew York.
  • BROWDER, F.E. (1968). The fixed point theory for multi-valued mappings in topological spaces. Math. Ann.. 177. 283-301
  • DEIMLING. (1985). Nonlinear Functional Analysis. Springer-Verlag.
  • DHAGE, B.C. (2005). Multi-valued mappings and fixed points I. Nonlinear Functional Anal., & Appl. 10. 359-378
  • DHAGE, B.C. (2006). Multi-valued mappings and fixed points II. Tamkang J. Math. 37. 27-46
  • DHAGE, B.C. (2008). Asymptotic stability of nonlinear functional integral equations via measures of noncompactness. Comm. Appl. Nonlinear...
  • HIMMELBERG, C.J. (1972). Fixed point for compact multifunctions. J. Math. Anal. Appl. 38. 205-207
  • HU, S,PAPAGEORGIOU, N.S. (1997). Handbook of Multivalued Analysis. Theory, Kluwer Academic Publishers. Dordrechet / Boston / London.
  • KAKUTANI, S. (1941). A generalization of Brower’s fixed point theorem. DukeMath. J. 8. 457-459
  • PETRUSEL, A. (2002). Operatorial Inclusions: House of the Book of Science. Cluj Napoka.
  • O’REGAN, D. (1998). Fixed point theory for closed multifunctions. Arch. Math. (Brno. 34. 191-197
  • SADOVSKII, B.N. (1972). Limit-compact and condensing operators. Russian Math. Survey. 27. 85-155