Some remarks on a fixed point property for multivalued mapping

• Autorzy: Kapeluszny J.
• Języki publikacji: PL

Abstrakty

EN

In [5] T. Dominguez Benavides and B. Gavira proved that Banach spaces with [wzór] satisfy the fixed point property for nonexpansive compact convex valued multivalued mappings. We give some simplification of the proof of this theorem.

Słowa kluczowe

PL

odwzorowanie wielowartościowe; punkt stały odwzorowania; odwzorowanie; gładkość jednostajna

EN

multivalued mappings; fixed-point property; nonexpansive mappings; uniform smoothness

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2010
• Tom: Vol. 32
• Strony: 47--52
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Kapeluszny J.

• Instytyt Matematyki UMCS, Pl. Marii Curie-Skodowskiej 1, 20-031 Lublin, Poland,

Bibliografia

• [1] A. G. Aksoy and M. A. Khamsi, Nonstandard methods in fixed point theory, Springer-Verlag, Berlin, 1990
• [2] T. Dominguez Benavides and B. Gavira, A universal infnite-dimensional modulus for normed spaces and applications, Nonlinear Anal. 58 (2004), 379-394.
• [3] C. Beniytez, K. Przeslawski and D. Yost, A universal modulus for normed spaces, Studia Math. 127(1) (1998), 21-46.
• [4] T. Dominguez Benavides and B. Gavira, A universal infinite-dimensional modulus with applications in fixed point theory, Proccedings of the International Conference on Fixed Point Theory and Applications, Valencia (2003), 27-40.
• [5] T. Dominguez Benavides and B. Gavira, The _xed point property for multivalued nonexpansive mappings, J. Math. Anal. Appl. 328 (2007), 379-394.
• [6] M. Edelstein, The construction of asymptotic center with a fixed point property, Bull. Amer. Math. Soc. 78 (1972), 206-208.
• [7] B. Gavira, Some moduli in Banach spaces with applications in metric fixed point theory, doctor thesis, University of Sevilla.
• [8] W. A. Kirk and S. Massa, Remarks on asymptotic and Chebyshev centers, Houston J. Math. 16 (1990), 357-364.
• [9] T. Kuczumow and S. Prus, Asymptotic centers and fixed points of multivalued nonexpansive mappings, Houston J. Math. 16 (1990), 465-468.
• [10] T. C. Lim, A _xed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach space, Proc. Amer. Math. Soc. 80 (1974), 1123-1126.
• [11] T. C. Lim, Characterizations of normal structure, Bull. Amer. Math. Soc. 43 (1974), 313-319.
• [12] S. B. Nadler, Multivalued contraction mappings, Pacific J. Math. 30 (1969), 475-488.
• [13] S. Prus, Some estimates for the normal structure coefficient in Banach spaces, Rend. Circ. Mat. Palermo XL (1991), 128-135.