scholarly journals Halpern iteration for strongly quasinonexpansive mappings on a geodesic space with curvature bounded above by one

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Yasunori Kimura ◽  
Kenzi Satô
Keyword(s):  
Geodesic Space ◽  
Halpern Iteration

Weighted higher order exponential type inequalities in metric spaces and applications

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Huiju Wang ◽  
Pengcheng Niu
Keyword(s):  
Homogeneous Space ◽  
Lie Groups ◽  
Sobolev Spaces ◽  
Exponential Type ◽  
Metric Spaces ◽  
Type Inequality ◽  
Higher Order ◽  
Geodesic Space ◽  
Stratified Lie Groups ◽  
Weighted Case

AbstractIn this paper, we establish weighted higher order exponential type inequalities in the geodesic space {({X,d,\mu})} by proposing an abstract higher order Poincaré inequality. These are also new in the non-weighted case. As applications, we obtain a weighted Trudinger’s theorem in the geodesic setting and weighted higher order exponential type estimates for functions in Folland–Stein type Sobolev spaces defined on stratified Lie groups. A higher order exponential type inequality in a connected homogeneous space is also given.

scholarly journals On the Halpern iteration in CAT(0) spaces

2015 ◽  
Vol 6 (3) ◽  
pp. 155-165
Author(s):  
Hadi Khatibzadeh ◽  
Sajad Ranjbar
Keyword(s):  
Halpern Iteration

scholarly journals Strong convergence of a composite Halpern-type iteration for a family of nonexpansive mappings in CAT(0) spaces

2017 ◽  
Vol 25 (3) ◽  
pp. 183-197
Author(s):  
Sajad Ranjbar
Keyword(s):  
Strong Convergence ◽  
Nonexpansive Mappings ◽  
Halpern Iteration

Abstract In this paper, we prove the strong convergence of the composite Halpern-type iteration for a family of nonexpansive mappings in CAT(0) spaces and compare our results with several recent results in this subject. Also, the inexact version of the Halpern iteration is studied in CAT(0) spaces.

scholarly journals Relaxation of Some Confusions about Confounders

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1450
Author(s):  
Ádám Zlatniczki ◽  
Marcell Stippinger ◽  
Zsigmond Benkő ◽  
Zoltán Somogyvári ◽  
András Telcs
Keyword(s):  
Dynamic Systems ◽  
Conditional Independence ◽  
Causal Discovery ◽  
Stochastic Dynamic ◽  
Geodesic Space ◽  
Independence Tests ◽  
Interacting Systems ◽  
Stochastic Dynamic Systems

This work is about observational causal discovery for deterministic and stochastic dynamic systems. We explore what additional knowledge can be gained by the usage of standard conditional independence tests and if the interacting systems are located in a geodesic space.

scholarly journals Asymptotic Behavior of Resolvents of a Convergent Sequence of Convex Functions on Complete Geodesic Spaces

Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 21
Author(s):  
Yasunori Kimura ◽  
Keisuke Shindo
Keyword(s):  
Asymptotic Behavior ◽  
Convex Functions ◽  
Lower Semicontinuous ◽  
Convergent Sequence ◽  
Lower Semicontinuous Function ◽  
Semicontinuous Function ◽  
Geodesic Space ◽  
Proper Convex ◽  
Convex Lower Semicontinuous Function ◽  
Sequence Of Functions

The asymptotic behavior of resolvents of a proper convex lower semicontinuous function is studied in the various settings of spaces. In this paper, we consider the asymptotic behavior of the resolvents of a sequence of functions defined in a complete geodesic space. To obtain the result, we assume the Mosco convergence of the sets of minimizers of these functions.

scholarly journals The Mann algorithm in a complete geodesic space with curvature bounded above

2013 ◽  
Vol 2013 (1) ◽  
pp. 336 ◽  
Author(s):  
Yasunori Kimura ◽  
Satit Saejung ◽  
Pongsakorn Yotkaew
Keyword(s):  
Geodesic Space ◽  
Mann Algorithm

scholarly journals Uniform Convexity and Convergence of a Sequence of Sets in a Complete Geodesic Space

2022 ◽  
Vol 2022 ◽  
pp. 1-11
Author(s):  
Yasunori Kimura ◽  
Shuta Sudo
Keyword(s):  
Uniform Convexity ◽  
Set Convergence ◽  
Geodesic Space ◽  
Metric Projections ◽  
Geodesic Spaces

In this paper, we first introduce two new notions of uniform convexity on a geodesic space, and we prove their properties. Moreover, we reintroduce a concept of the set-convergence in complete geodesic spaces, and we prove a relation between the metric projections and the convergence of a sequence of sets.

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