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Henryk Hudzik : vita et opera

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This article contains a short vita of Henryk Hudzik's as well as a non-exhaustive survey of his contribution to various areas of analysis. We focus on the theory of Orlicz−Sobolev spaces and the geometry of Banach spaces. We highlight criteria for some important geometric properties related to the metric fixed point theory in some classes of Banach lattices, including Orlicz and Orlicz−Lorentz spaces, but we do not forget Henryk Hudzik's contribution to nonlinear integral equations and partial differential equations.
Słowa kluczowe
Rocznik
Strony
45--78
Opis fizyczny
Bibliogr. 36 poz., fot.
Twórcy
autor
  • Faculty of Mathematics and Computer Sciences, Adam Mickiewicz University in Poznań, ul. Umultowska 87, 61-614 Poznan, Poland
autor
  • Faculty of Mathematics and Computer Sciences, Adam Mickiewicz University in Poznań, ul. Umultowska 87, 61-614 Poznan, Poland
Bibliografia
  • [1]. Ł A. Adams, Sobolev Spaces, Academic Press, New York 1975.
  • [2]. M. A. Akcoglu and L. Sucheston, On uniform monotonicity of norms and ergodic theorems in function maces. Rend. Circ. Mat. 8 (1985), no. 2, 325-335.
  • [3]. Z. Altschuler, Uniform convexity in Lorentz sequence spaces, Israel J. Math. 20 (1975), 260-274, DOI 10.1007/BF02760331.
  • [4]. Beck, A convexity condition in Banach spaces and the strong law of large numbers, Proc. Amer. Math. Soc. 13 (1962), 329-334.
  • [5]. G. Birkhoff, Lattice Theory, Amer. Math. Soc., Providence, RI1979.
  • [6]. P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113-190.
  • [7]. M. M. Day, Some more uniformly convex spaces, Bull. Am. Math. Soc. 47 (1941), 504-507.
  • [8]. D. J. Dowling and B. Turett, Some properties of the characteristic of convexity relating to fixed point theory, Pac. J. Math. 104 (1983), 343-350.
  • [9]. J Elton and E. Odell, The unit ball of every infinite-dimensional normed linear space contains a (1 +ε)-separated sequence, Colloq. Math. 44 (1981), no. no. 1,105-109.
  • [10]. P Enflo, Banach spaces which can be given an equivalent uniformly convex norm, Israel J. Math. 13 (1972), 281-288.
  • [11]. H. G Feichtinger, Modulation spaces on locally compact Abelian group Technical Report, University of Sterna 1983, Proc. Internat. Conf. on Wavelet and Applications, New Delhi Allied Publishers, India, 2003, 99-140.
  • [12]. J. Garcia-Falset, Stability and fixed points for nonexpansive mappings, Houston J. Math. 20 (1994), no. 3, 495-506.
  • [13]. J. Garcia-Falset, E. Llorens-Fuster, and E. M. Mazcuñan-Navarro, Uniformly nonsquare Banach spaces hue the fixed point property for nonexpansive mappings, J. Funct. Anal. 233 (2006), no. 2, 494-514, DOI K)J016/j.jfa.2005.09.002.
  • [14]. K. Goebel and W. A. Kirk, Topics in metric fixed point theory, Cambridge University Press, Cambridge 1990.
  • [15]. I. Halperin, Uniform convexity in function spaces, Duke Math. J. 21 (1954), 195-204.
  • [16]. R. Huff, Banach spaces which are nearly uniformly convex, Rocky Mountain J. Math. 10 (1980), no. 4, 743-794, DOI 10.1216/RMJ-1980-10-4-743.
  • [17]. R. C. James, Uniformly non-square Banach spaces, Ann. Math. 80 (1964), 542-550.
  • [18]. R. C. James, Super-reflexive Banach spaces, Can. J. Math. 24 (1972), 896-904.
  • [19]. N. Kalton and S. Montgomery-Smith, Interpolation of Banach spaces (W. B. Johnson and J. Lindenstrauss, eds.), Handbook of Geometry of Banach Spaces, vol. 2, Elsevier, Amsterdam, 2003,1131-1175.
  • [20]. A. Kamińska, On uniform convexity of Orlicz spaces, Indag. Math. 44 (1982), no. 1, 27-36.
  • [21]. W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004-1006.
  • [22]. C. A. Kottman, Packing and reflexivity in Banach spaces, Trans. Amer. Math. Soc. 150 (1970), 565-576.
  • [23]. W. Kurc, Strictly and uniformly monotone Musielak-Orlicz spaces and applications to best approximation, J. Approx. Theory 69 (1992), no. 2,173-187, DOI 10.1016/0021-9045(92)90141-A.
  • [24]. D. Kutzarova, k-β and k-nearly uniformly convex Banach spaces, J. Math. Anal. Appl. 162 (1991), no. 2, 322-338, DOI 10.1016/0022-247X(91)90153-Q.
  • [25]. V. I. Liokumovich, The existence of B-spaces with non-convex modulus of convexity, Izv. Vyss Ućebn. Zaved. Mathematika 12 (1973), 43-50; in Russian.
  • [26]. G. Ya. Lozanovskii, On some Banach lattices, Sibirs. Math. Z. 10 (1969), 584-599; English transl., Siberian Math. J. 10 (1969), 419-431.
  • [27]. Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597.
  • [28]. V. I. Ovchinnikov, The method of orbits in interpolation theory, Math. Rep. 1 (1984), no. 2, 349-515.
  • [29]. G. Pisier, Some applications of the complex interpolation method to Banach lattices, J. Analyse Math. 35(1979), 264-281, DOI 10.1007/BF02791068.
  • [30]. S. Prus, Multi-dimensional uniform convexity and uniform smoothness of Banach spaces, Recent advances on metric fixed point theory (Seville, Spain, 1995), Ciencias, vol. 48, Univ. Sevilla, Seville, 1996, 111-136.
  • [31]. S. Reisner, On two theorems of Lozanovskii concerning intermediate Banach lattices, Lecture Notes in Mathematics, vol. 1317, Springer Verlag, 57-83.
  • [32]. S. Rolewicz, On A-uniform convexity and drop property, Studia Math. 87 (1987), no. 2, 181-191.
  • [33]. M. A. Smith and B. Turett, Rotundity in Lebesgue-Bochner function spaces, Trans. Amer. Math. Soc. 257(1980), no. 1, 105-118, DOI 10.2307/1998127.
  • [34]. K. Sundaresan, Uniformly non-l_n Orlicz spaces, Israel J. Math. 3 (1965), 139-146.
  • [35]. N. Trudinger, On imbeddings into Orlicz spaces and some applications, J. Math. Mech. 17 (1967), 473-483.
  • [36]. L. C. Young, General inequalities for Stieltjes integrals and the convergence of Fourier series, Math. Ann. 115 (1938), no. 1, 581-612, DOI 10.1007/BF01448958.
Uwagi
Zawiera wykaz wszystkich publikacji Henryka Hudzika
The complete list of Henryk Hudzik's papers
Typ dokumentu
Bibliografia
Identyfikator YADDA
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