Busemann Spaces and Hyperbolic Spaces

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

Chapter Chapter 6 in Fixed Point Theory in Distance Spaces, 2014, pp 39-45 from Springer

Abstract: Abstract A Busemann space geodesic space Busemann space (also known as a Busemann convex space) is a geodesic metric space X such that for any two geodesics γ : a , b → X $$\gamma: \left [a,b\right ] \rightarrow X$$ and γ ′ : a ′ , b ′ → X , $$\gamma ^{{\prime}}: \left [a^{{\prime}},b^{{\prime}}\right ] \rightarrow X,$$ the map D γ , γ ′ : a , b × a ′ , b ′ → ℝ $$D_{\gamma,\gamma ^{{\prime}}}: \left [a,b\right ] \times \left [a^{{\prime}},b^{{\prime}}\right ] \rightarrow \mathbb{R}$$ defined by D γ , γ ′ t , t ′ = d γ t , γ ′ t ′ $$\displaystyle{ D_{\gamma,\gamma ^{{\prime}}}\left (t,t^{{\prime}}\right ) = d\left (\gamma \left (t\right ),\gamma ^{{\prime}}\left (t^{{\prime}}\right )\right ) }$$ is convex.

Keywords: Convex Hull; Topological Space; Initial Point; Differential Geometry; Convex Combination (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-10927-5_6

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