Previous |  Up |  Next


measure of noncompactness; near convexity; the property of strong $(\alpha ')$
The aim of this paper is to derive some relationships between the concepts of the property of strong $(\alpha ')$ introduced recently by Hong-Kun Xu and the so-called characteristic of near convexity defined by Goebel and S\c ekowski. Particularly we provide very simple proof of a result obtained by Hong-Kun Xu.
[1] Banaś J.: On drop property and nearly uniformly smooth Banach spaces. Nonlinear Analysis T.M.A. 14 (1990), 927-933. MR 1058414
[2] Banaś J.: Compactness conditions in the geometric theory of Banach spaces. Nonlinear Analysis T.M.A. 16 (1991), 669-682. MR 1097324
[3] Banaś J., Frączek K.: Conditions involving compactness in geometry of Banach spaces. Nonlinear T.M.A. 20 (1993), 1217-1230. MR 1219238
[4] Banaś J., Goebel K.: Measures of Noncompactness in Banach Spaces. Lecture Notes in Pure and Applied Math., vol. 60, M. Dekker, New York, Basel, 1980. MR 0591679
[5] Daneš J.: A geometric theorem useful in nonlinear analysis. Boll. Un. Mat. Ital. 6 (1972), 369-372. MR 0317130
[6] Daneš J.: On densifying and related mappings and their application in nonlinear functional analysis. Theory of Nonlinear Operators, Akademie-Verlag, Berlin, 1974, pp. 15-56. MR 0361946
[7] Garcia-Falset J., Jimenez-Melado A., Llorens-Fuster E.: A characterization of normal structure in Banach spaces. Fixed Point Theory and Applications (K.K. Tan, ed.), World Scientific, Singapore, 1992, pp. 122-129.
[8] Goebel K., Sȩkowski T.: The modulus of noncompact convexity. Ann. Univ. Mariae Curie- Skłodowska, Sect. A 38 (1984), 41-48. MR 0856623
[9] Hong-Kun Xu: Measures of noncompactness and normal type structures in Banach spaces. Panamer. Math. J. 3 (1993), 17-34. MR 1216273 | Zbl 0846.46008
[10] Köthe G.: Topological Vector Spaces I. Springer Veralg, Berlin, 1969. MR 0248498
[11] Lindenstrauss J., Tzafiri L.: Classical Banach Spaces. Springer Verlag, Berlin, 1973. MR 0415253
[12] Montesinos V.: Drop property equals reflexivity. Studia Math. 87 (1987), 93-110. MR 0924764 | Zbl 0652.46009
[13] Rolewicz S.: On drop property. Studia Math. 85 (1987), 27-35. MR 0879413
Partner of
EuDML logo