On Some Applications of Geometry of Banach Spaces and Some New Results Related to the Fixed Point Theory in Orlicz Sequence Spaces  

作　　者：Yunan Cui Henryk Hudzik Radosław Kaczmarek Haifeng Ma Yuwen Wang Meiling Zhang 

机构地区：[1]Department of Mathematics,Harbin University of Science and Technology,Harbin 150080,P.R.China [2]Faculty of Economics and Information Technology,The State University of Applied Sciences in Płock,Nowe Trzepowo 55,09-402 Płock,Poland [3]Faculty of Mathematics and Computer Science,Adam Mickiewicz University in Pozna´n,Umultowska 87,61-614 Poznan,Poland [4]School of Mathematical Science,Harbin Normal University,Harbin 150025,P.R.China

出　　处：《Journal of Mathematical Study》2016年第4期325-378,共54页数学研究（英文）

基　　金：The first author gratefully acknowledges the support of the Natural Science Foundation of Heilongjiang Province of China(A2015018);The authors are grateful to Professor Grzegorz Lewicki for his information concerning the proofs of Lemma 2.3 and Theorem 2.4.The fourth author Haifeng Ma gratefully acknowledges the support the National Natural Science Foundation of China(Grant No.11401143);Overseas Returning Foundation of Hei Long Jiang Province(Grant No.LC201402);The fifth author Yuwen Wang gratefully acknowledges the support of the National Natural Science Foundation of China(Grant No.11471091).

摘　　要：We present some applications of the geometry of Banach spaces in the approximation theory and in the theory of generalized inverses.We also give some new results,on Orlicz sequence spaces,related to the fixed point theory.After a short introduction,in Section 2 we consider the best approximation projection from a Banach space X onto its non-empty subset and proximinality of the subspaces of order continuous elements in various classes of Kothe spaces.We present formulas for the distance to these subspaces of the elements exterior to them.In Section 3 we recall some results and definitions concerning generalized inverses of operators(metric generalized inverses and Moore-Penrose generalized inverses).We also recall some results on the perturbation analysis of generalized inverses in Banach spaces.The last part of this section concerns generalized inverses of multivalued linear operators(their definitions and representations).The last section starts with a formula for modulus of nearly uniform smoothness of Orlicz sequence spacesℓ^(Φ)equipped with the Amemiya-Orlicz norm.From this result a criterion for nearly uniform smoothness of these spaces is deduced.A formula for the Dom´ınguez-Benavides coefficient R(a,l_(Φ))is also presented,whence a sufficient condition for the weak fixed point property of the spaceℓ^(Φ)is obtained.

关 键 词：Approximative compactness proximinality Kadec-Klee property uniform rotundity Orlicz spaces Banach lattices quasi-linear projection generalized inverses 

分 类 号：O17[理学—数学]