In this paper, we give necessary and sufficient conditions for a point in a Musielak-Orlicz sequence space equipped with the Orlicz norm to be an {\bf H}-point. We give necessary and sufficient conditions for a Musielak-Orlicz sequence space equipped with the Orlicz norm to have the {\it Kadec-Klee} property, the uniform {\it Kadec-Klee} property and to be nearly uniformly convex. We show that a Musielak-Orlicz sequence space equipped with the Orlicz norm has the fixed point property if and only if it is reflexive.
@article{119244, author = {Harold Bevan Thompson and Yunan Cui}, title = {The fixed point property in Musielak-Orlicz sequence spaces}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {42}, year = {2001}, pages = {299-309}, zbl = {1056.46021}, mrnumber = {1832148}, language = {en}, url = {http://dml.mathdoc.fr/item/119244} }
Thompson, Harold Bevan; Cui, Yunan. The fixed point property in Musielak-Orlicz sequence spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 299-309. http://gdmltest.u-ga.fr/item/119244/
Geometry of Orlicz spaces, Dissertation Math., Warsaw, 1996. | MR 1410390 | Zbl 1089.46500
Maluta coefficient and Opial property in Musielak-Orlicz sequence spaces equipped with the Luxemburg norm, Nonlinear Anal. Theory Methods & Appl., to appear. | MR 1656529
Some geometric properties in Orlicz sequence spaces equipped with the Orlicz norm, J. Convex Anal. 6 (1999), 91-113. (1999) | MR 1713953
Uniformly non-$l_n^{(1)}$ Musielak-Orlicz sequence spaces, Proc. Indian. Acad. Sci. 101.2 (1991), 71-86. (1991) | MR 1125480
Sequence and Series in Banach Spaces, Graduate Texts in Math. 92, Springer-Verlag, 1984. | MR 0737004
Reflexivity and the fixed-point property for nonexpansive maps, J. Math. Anal. Appl. 200 (1996), 653-662. (1996) | MR 1393106 | Zbl 0863.47038
Fixed points of nonexpansive mappings and Chebyshev centers in Banach spaces with norms of type (KK), Banach Space Theory and its Applications (Bucharest, 1981), pp.35-43; Lecture Notes in Math. 991, Springer, Berlin-New York, 1983. | MR 0714171 | Zbl 0512.46015
The modulus of non-compact convexity, Ann. Univ. Maria Curie-Sklodowska, Sect. A 38 (1984), 41-48. (1984) | MR 0856623
Topics in Metric Fixed Point Theory, Cambridge University Press, 1990. | MR 1074005
Some remarks on convergence in Orlicz spaces, Comment. Math. 21 (1979), 81-88. (1979) | MR 0577673
Support functionals and smoothness in Musielak-Orlicz sequence spaces equipped with the Luxemburg norm, Comment. Math. Univ. Carolinae 31.4 (1990), 661-684. (1990) | MR 1091364
Banach spaces which are nearly uniformly convex, Rocky Mountain J. Math. 10 (1980), 473-749. (1980) | MR 0595102 | Zbl 0505.46011
Relations between some properties of convexity of the ball of a Banach spaces, Functional Anal. Appl. 16 (1982), 93-100. (1982)
Uniform rotundity of Musielak-Orlicz sequence spaces, J. Approx. Theory 47.4 (1986), 302-322. (1986) | MR 0862227 | Zbl 0606.46003
Flat Orlicz-Musielak sequence spaces, Bull. Acad. Polon. Sci. Math. 30 (1982), 347-352. (1982) | MR 0707748 | Zbl 0513.46008
Functional Analysis (in Russian), 2nd edition, Moscow, 1978. | MR 0511615
Orlicz spaces and modular spaces, Lecture Notes in Math. 1034, Springer Verlag, Berlin, 1983. | MR 0724434 | Zbl 0557.46020
H-point and denting points in Orlicz spaces, Comment. Math. 33 (1993), 135-151. (1993) | MR 1269408
Theory of Orlicz spaces, Marcel Dekker Inc., New York, Basel, HongKong, 1991. | MR 1113700 | Zbl 0724.46032
Norm calculations and complex rotundity of Musielak-Orlicz sequence spaces, Chinese Math. Ann. 12A (Special Issue) 98-102.