Length Spaces and Local Contractions

William Kirk and Naseer Shahzad
Additional contact information
William Kirk: University of Iowa, Department of Mathematics
Naseer Shahzad: King Abdulaziz University, Department of Mathematics

Chapter Chapter 7 in Fixed Point Theory in Distance Spaces, 2014, pp 47-59 from Springer

Abstract: Abstract In general, a path in a metric space X , d $$\left (X,d\right )$$ is a continuous image of the unit interval I = 0 , 1 ⊂ ℝ . $$I = \left [0,1\right ] \subset \mathbb{R}.$$ If S ≡ f I $$S \equiv f\left (I\right )$$ is a path, then its length is defined as ℓ S = sup x i ∑ i = 0 N − 1 d f x i , f x i + 1 $$\displaystyle{ \ell\left (S\right ) =\sup _{\left (x_{i}\right )}\sum _{i=0}^{N-1}d\left (f\left (x_{ i}\right ),f\left (x_{i+1}\right )\right ) }$$ where x i : = 0 = x 0

Keywords: Banach Space; Bounded Sequence; Usual Sense; Length Space; Preserve Function (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-10927-5_7

Ordering information: This item can be ordered from
http://www.springer.com/9783319109275

DOI: 10.1007/978-3-319-10927-5_7

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().