A note on the measure of solvability

• Autorzy: Caponetti D. , Trombetta G.
• Języki publikacji: EN

Abstrakty

EN

Let X be an infinite-dimensional Banach space. The measure of solvability v(I) of the identity operator I is equal to 1.

Słowa kluczowe

EN

minimal displacement; measure of noncompactness; (psi)k-set contraction; measure of solvability

PL

przesunięcie minimalne; miara niezwartości; miara rozwiązalności

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 2
• Strony: 179--183
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Caponetti D.

• Dipartimento di Matematica e Applicazioni, Università di Palermo, Via Archirafi 34, I-90123 Palermo, Italy

autor

Trombetta G.

• Dipartimento di Matematica, Università della Calabria, I-87036 Arcavacata di Rende (CS), Italy

Bibliografia

• [1] R. R. Akhmerov, M. I. Kamenskiĭ, A. S. Potapov, A. E. Rodkina and B. N. Sadovskii, Measures of Noncompactness and Condensing Operators, Birkhäuser, Basel, 1992.
• [2] Y. Benyamini and Y. Sternfeld, Spheres in infinite-dimensional normed spaces are Lipschitz contractible, Proc. Amer. Math. Soc. 88 (1983), 439-445.
• [3] K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, New York, 1985.
• [4] W. Feng, A new spectral theory for nonlinear operators and its applications, Abstr. Appl. Anal. 2 (1997), 163-183.
• [5] M. Furi and M. Martelli, On α-Lipschitz retractions of the unit closed ball onto its boundary, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 57 (1974), 61-65.
• [6] K. Goebel, On the minimal displacement of points under Lipschitzian mappings, Pacific J. Math. 45 (1973), 135-140.
• [7] K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge Univ. Press, Cambridge, 1990.
• [8] P. K. Lin and Y. Sternfeld, Convex sets with the Lipschitz fixed point property are compact, Proc. Amer. Math. Soc. 93 (1985), 633-639.
• [9] B. Nowak, On the Lipschitzian retraction of the unit ball in infinite-dimensional Banach spaces onto its boundary, Bull. Acad. Polon. Sci. 27 (1979), 861-864.
• [10] M. Väth, Volterra and Integral Equations of Vector Functions, Monogr. Textbooks Pure Applied Math. 224, Dekker, New York.
• [11] -, Fixed point free maps of a closed ball with small measures of noncompactness, Collect. Math. 52 (2001), 101-116.