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Remarks on a recent paper titled: 'On the split common fixed point problem for strict pseudocontractive and asymptotically nonexpansive mappings in Banach spaces'
- Source :
- Journal of Inequalities and Applications, Vol 2021, Iss 1, Pp 1-5 (2021)
- Publication Year :
- 2021
- Publisher :
- SpringerOpen, 2021.
-
Abstract
- In a recently published theorem on the split common fixed point problem for strict pseudocontractive and asymptotically nonexpansive mappings, Tang et al. (J. Inequal. Appl. 2015:305, 2015) studied a uniformly convex and 2-uniformly smooth real Banach space with the Opial property and best smoothness constant κ satisfying the condition $0 0 < κ < 1 2 , as a real Banach space more general than Hilbert spaces. A well-known example of a uniformly convex and 2-uniformly smooth real Banach space with the Opial property is $E=l_{p}$ E = l p , $2\leq p 2 ≤ p < ∞ . It is shown in this paper that, if κ is the best smoothness constant of E and satisfies the condition $0 0 < κ ≤ 1 2 , then E is necessarily $l_{2}$ l 2 , a real Hilbert space. Furthermore, some important remarks concerning the proof of this theorem are presented.
- Subjects :
- Pure mathematics
Smoothness (probability theory)
Applied Mathematics
lcsh:Mathematics
Banach space
Hilbert space
Regular polygon
010103 numerical & computational mathematics
Fixed point
lcsh:QA1-939
01 natural sciences
Opial property
010101 applied mathematics
symbols.namesake
Accretive
Uniformly smooth
Common fixed point
symbols
Discrete Mathematics and Combinatorics
0101 mathematics
Constant (mathematics)
Analysis
Mathematics
Subjects
Details
- Language :
- English
- Volume :
- 2021
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Journal of Inequalities and Applications
- Accession number :
- edsair.doi.dedup.....2d355d55a97da33d4c96cf2b0a89eb42