@Article{JMS-49-4,
author = {Yunan, Cui and Hudzik, Henryk and Radosław, Kaczmarek and Ma, Haifeng and Yuwen, Wang and Zhang, Meiling},
title = {On Some Applications of Geometry of Banach Spaces and Some New Results Related to the Fixed Point Theory in Orlicz Sequence Spaces},
journal = {Journal of Mathematical Study},
year = {2016},
volume = {49},
number = {4},
pages = {325--378},
abstract = {<p style="text-align: justify;">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 Köthe spaces. We present formulas for the distance to these subspaces of
the elements from the outside of 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 spaces $\ell^\Phi$&nbsp;equipped with the Amemiya-Orlicz norm.
From this result a criterion for nearly uniform smoothness of these spaces is deduced.
A formula for the Domínguez-Benavides coefficient $R(a,l_\Phi)$ is also presented, whence
a sufficient condition for the weak fixed point property of the space $\ell^\Phi$&nbsp;is obtained.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v49n4.16.02},
url = {https://global-sci.com/article/87809/on-some-applications-of-geometry-of-banach-spaces-and-some-new-results-related-to-the-fixed-point-theory-in-orlicz-sequence-spaces}
}