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The generalized Day norm. Part I. Properties

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In this paper we introduce a modification of the Day norm in \(c_0(\Gamma)\) and investigate properties  of this norm.
Opis fizyczny
  • Boas, R. P., Jr., Some uniformly convex spaces, Bull. Amer. Math. Soc. 46 (1940), 304-311.
  • Baillon, J.-B., Schoneberg, R., Asymptotic normal structure and fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 81 (1981), 257-264.
  • Brodskii, M. S., Mil’man, D. P., On the center of a convex set, Doklady Akad. Nauk SSSR (N.S.) 59 (1948), 837-840.
  • Clarkson, J. A., Unifomly convex spaces, Trans. Amer. Math. Soc. 78 (1936), 396-414.
  • Day, M. M., Strict convexity and smoothness of normed spaces, Trans. Amer. Math. Soc. 78 (1955), 516-528.
  • Day, M. M., James, R. C., Swaminathan, S., Normed linear spaces that are uniformly convex in every direction, Canad. J. Math. 23 (1971), 1051-1059.
  • Dodds, P. G., Dodds, T. K., Sedaev, A. A., Sukochev, F. A., Local uniform convexity and Kadec-Klee type properties in K-interpolation spaces. I: General theory, J. Funct. Spaces Appl. 2 (2004), 125-173.
  • Garkavi, A. L., On the optimal net and best cross-section of a set in a normed space (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 26 (1962), 87-106.
  • Goebel, K., Kirk, W. A., Topics in Metric Fixed Point Theory, Cambridge University Press, 1990.
  • Goebel, K., Reich, S., Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Marcel Dekker, 1984.
  • Hanner, O., On the uniform convexity of \(L^p\) and \(l^p\), Ark. Mat. 3 (1956), 239-244.
  • Holmes, R. B., Geometric Functional Analysis and Its Applications, Springer, 1975.
  • Kirk, W. A., A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004-1006.
  • Lovaglia, A. R., Locally uniformly convex Banach spaces, Trans. Amer Math. Soc. 78 (1955), 225-238.
  • Maluta, E., A diametrically complete set with empty interior in a reflexive LUR space, J. Nonlinear Conv. Anal. 18 (2017),105-111.
  • Mariadoss, S. A., Soardi, P. M., A remark on asymptotic normal structure in Banach spaces, Rend. Sem. Mat. Univ. Politec. Torino 44 (1986), 393-395.
  • Opial, Z., Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597.
  • Rainwater, J., Local uniform convexity of Day’s norm on \(c_0(\Gamma)\), Proc. Amer. Math. Soc. 22 (1969), 335-339.
  • Smith, M. A., Some examples concerning rotundity in Banach spaces, Math. Ann. 233 (1978), 155-161.
  • Smith, M. A., Turett, B., A reflexive LUR Banach spaces that lacks normal structure, Canad. Math. Bull. 28 (1985), 492-494.
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