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Maluta’s coefficient and Opial’s properties in Musielak-Orlicz sequence spaces equipped with the Luxemburg norm. (English) Zbl 0922.46005
Consider $\varphi =(\varphi _{i})_{i=1}^{\infty }$ a Musielak-Orlicz function (i.e. $\varphi _{i}$ is a Orlicz function for every $i$) and $\ell ^{\varphi }=\{x\in \ell ^{0}\mid \sum_{i=1}^{\infty }\varphi _{i}(\lambda x_{i})<\infty $ for some $\lambda >0\}$ the Musielak-Orlicz sequence space. In the main results of the paper, when $\varphi $ is finitely valued and satisfies condition (*), the authors show that the Opial properties for $\ell ^{\varphi }$ are equivalent to the $\delta_2$ condition, and they give expressions for Maluta’s coefficient $D(\ell ^{\varphi })$ when $\ell ^{\varphi }$ is nonreflexive and reflexive, respectively.

46A45Sequence spaces
Full Text: DOI
[1] Ayerbe, J. M.; Benavides, T. D.: Connections between some Banach space coefficients concerning normal structure. J. math. Anal. appl. 172, 53-61 (1993) · Zbl 0790.46011
[2] M.S. Brodskiı\breve{}, D.P. Millman, On the center of a convex set, Dokl. Acad. Nauk SSSR 59 (1948) 837--840.
[3] Bynum, W. L.: Normal structure coefficients for Banach spaces. Pacific J. Math. 86, 427-436 (1980) · Zbl 0442.46018
[4] Denker, M.; Hudzik, H.: Uniformly non-$ln(1)$ Musielak--Orlicz sequence spaces. Proc. indian acad. Sci. 101, No. 2, 71-86 (1991) · Zbl 0789.46008
[5] Benavides, T. D.: Weak uniform normal structure in direct-sum spaces. Studia math. 103, 293-293 (1992)
[6] T.D. Benavides, G.L. Acedo, Lower bounds for normal structure coefficients, Proc. Roy. Soc. Edinburg 121 A (1992) 245--252. · Zbl 0787.46010
[7] T.D. Benavides, G.L. Acedo, Hong-Kun Xu, Weak uniform normal structure and iterative fized points of nonexpansive mappings, Colloquium Math. 68 (1) (1995) 17--23. · Zbl 0845.46006
[8] K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985. · Zbl 0559.47040
[9] D. Van Dulst, B. Sims, Lect. Notes Math., vol. 991, 35--43.
[10] R. Goebel, W.A. Kirk, Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge, 1990. · Zbl 0708.47031
[11] H. Hudzik, Yi.N. Ye, Support functionals and smoothness in Musielak--Orlicz sequence spaces endowed with the Luxemburg norm, Comment. Math. Unv. Carolinae 31 (4) (1990) 661--684. · Zbl 0721.46012
[12] H. Hudzik, C.X. Wu, Yi.N. Ye, Packing constant in Musielak--Orlicz sequence spaces equipped with the Luxemburg norm, Revista Math. 7 (1) (1994) 13--26. · Zbl 0818.46014
[13] Kirk, W. A.: A fixed point theorem for mappings which do not increase distances. Amer. math. Month. 72, 1004-1006 (1965) · Zbl 0141.32402
[14] Landes, T.: Permanence properties of normal structure. Pacific J. Math. 110, No. 1, 125-143 (1984) · Zbl 0534.46015
[15] Lim, T. C.: On the normal structure coefficient and the bounded sequence coefficient. Proc. amer. Math. soc. 88, 262-264 (1983) · Zbl 0541.46017
[16] Kaminska, A.: Flat Orlicz--Musielak sequence spaces. Bull. acad. Polon. sci. Math. 30, No. 7--8, 347-352 (1982) · Zbl 0513.46008
[17] Kaminska, A.: Uniform rotundity of Musielak--Orlicz sequence spaces. J. approx. Theory 47, No. 4, 302-322 (1986) · Zbl 0606.46003
[18] M.A. Krasnoselskiı\breve{}, Ya.B. Rutickiı\breve{}, Convex Functions and Orlicz Spaces (translation), Groningen, 1961.
[19] Kuratowski, K.: Sur LES espaces completes. Fund. math. 15, 301-309 (1930) · Zbl 56.1124.04
[20] W.A.J. Luxemburg, Banach Function Spaces, Thesis, Delft 1955. · Zbl 0068.09204
[21] L. Maligranda, Orlicz Spaces and Interpolation, Seminars in Mathematics, vol. 5, Campinas, 1989. · Zbl 0874.46022
[22] Maluta, E.: Uniformly normal structure and related coefficients. Pacific J. Math. 111, No. 2, 357-369 (1984) · Zbl 0495.46012
[23] J. Musielak, Orlicz Spaces and Modular-Spaces, Lecture Notes in Mathematics, vol. 1034, Springer, Berlin, 1983. · Zbl 0557.46020
[24] Prus, S.: Banach spaces with uniform Opial property. Nonlinear anal. Theory appl. 18, No. 8, 697-704 (1992) · Zbl 0786.46023
[25] M.M. Rao, Z.D. Ren, Theory of Orlicz Spaces, Marcel Dekker, New York, 1991. · Zbl 0724.46032
[26] Xu, H. K.: On the maluta problem of sequence constant in Banach spaces. Bull. sci. China 34, 725-726 (1989)
[27] Zhang, G. L.: Weakly convergent sequence coefficient of product space. Proc. amer. Math. soc. 117, 637-643 (1992) · Zbl 0787.46021