scholarly journals On weak uniform normal structure in weighted Orlicz sequence spaces

2008 ◽  
Vol 341 (2) ◽  
pp. 1042-1054 ◽  
Author(s):  
B. Zlatanov
Keyword(s):  
Normal Structure ◽  
Sequence Spaces ◽  
Uniform Normal Structure ◽  
Orlicz Sequence Spaces

(KK)-Properties, Normal Structure and Fixed Points of Nonexpansive Mappings in Orlicz Sequence Spaces

1986 ◽  
Vol 38 (3) ◽  
pp. 728-750 ◽  
Author(s):  
D. van Dulst ◽  
V. de Valk
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Orlicz Function ◽  
Normal Structure ◽  
Point Theory ◽  
Sequence Spaces ◽  
Orlicz Sequence Space ◽  
Orlicz Sequence Spaces ◽  
Vector Valued

In this paper we investigate Orlicz sequence spaces with regard to certain geometric properties that have proved to be important in fixed point theory. In particular, we shall consider various Kadec-Klee type properties, and weak and weak* normal structure. It turns out that many of these properties, though generally distinct, coincide in Orlicz sequence spaces and that all of them are intimately related to the so-called Δ2-condition. Some of our results extend to vector-valued Orlicz sequence spaces. For example, we prove a rather powerful theorem on the preservation of weak normal structure under the formation of substitution spaces. There is also a fixed point theorem: the Orlicz sequence space hM has the fixed point property if the complementary Orlicz function M* satisfies theΔ2-condition. Another one of our results implies that, under this assumption on M*, hM has weak normal structure if and only if M also satisfies the Δ2-condition.

Weakly compact sets in Orlicz sequence spaces

2021 ◽  
pp. 1-14
Author(s):  
Siyu Shi ◽  
Zhongrui Shi ◽  
Shujun Wu
Keyword(s):  
Sequence Spaces ◽  
Compact Sets ◽  
Weakly Compact ◽  
Orlicz Sequence Spaces ◽  
Weakly Compact Sets

scholarly journals On the modulus ofU-convexity

2005 ◽  
Vol 2005 (1) ◽  
pp. 59-66 ◽  
Author(s):  
Satit Saejung
Keyword(s):  
Banach Space ◽  
Dual Space ◽  
Normal Structure ◽  
Uniform Normal Structure

We prove that the moduli ofU-convexity, introduced by Gao (1995), of the ultrapowerX˜of a Banach spaceXand ofXitself coincide wheneverXis super-reflexive. As a consequence, some known results have been proved and improved. More precisely, we prove thatuX(1)>0implies that bothXand the dual spaceX∗ofXhave uniform normal structure and hence the “worth” property in Corollary 7 of Mazcuñán-Navarro (2003) can be discarded.

scholarly journals Local rotundity structure of Cesàro–Orlicz sequence spaces

2008 ◽  
Vol 345 (1) ◽  
pp. 410-419 ◽  
Author(s):  
Paweł Foralewski ◽  
Henryk Hudzik ◽  
Alicja Szymaszkiewicz
Keyword(s):  
Sequence Spaces ◽  
Orlicz Sequence Spaces

Fixed point theorems for uniformly generalized Kannan type semigroup of self-mappings

2017 ◽  
Vol 26 (2) ◽  
pp. 231-240
Author(s):  
AHMED H. SOLIMAN ◽  
MOHAMMAD IMDAD ◽  
MD AHMADULLAH
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Convex Subset ◽  
Fixed Point Theorems ◽  
Real Banach Space ◽  
Normal Structure ◽  
Uniform Normal Structure

In this paper, we consider a new uniformly generalized Kannan type semigroup of self-mappings defined on a closed convex subset of a real Banach space equipped with uniform normal structure and employ the same to show that such semigroup of self-mappings admits a common fixed point provided the underlying semigroup of self-mappings has a bounded orbit.

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