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

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.

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A modified Krasnosellkii-Mann algorithms for computing fixed points of multivalued quasi-nonexpansive mappings in Banach spaces

Creative Mathematics and Informatics ◽

10.37193/cmi.2019.02.10 ◽

2019 ◽

Vol 28 (2) ◽

pp. 191-198

Author(s):

T. M. M. SOW

Keyword(s):

Strong Convergence ◽

Fixed Points ◽

Banach Spaces ◽

Iterative Scheme ◽

Nonexpansive Mappings ◽

Mann Iteration ◽

Infinite Dimensional ◽

Mann Algorithm

It is well known that Krasnoselskii-Mann iteration of nonexpansive mappings find application in many areas of mathematics and know to be weakly convergent in the infinite dimensional setting. In this paper, we introduce and study an explicit iterative scheme by a modified Krasnoselskii-Mann algorithm for approximating fixed points of multivalued quasi-nonexpansive mappings in Banach spaces. Strong convergence of the sequence generated by this algorithm is established. There is no compactness assumption. The results obtained in this paper are significant improvement on important recent results.

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Inertial Krasnoselskii–Mann Method in Banach Spaces

Mathematics ◽

10.3390/math8040638 ◽

2020 ◽

Vol 8 (4) ◽

pp. 638

Author(s):

Yekini Shehu ◽

Aviv Gibali

Keyword(s):

Weak Convergence ◽

Banach Spaces ◽

Hilbert Spaces ◽

Nonexpansive Mappings ◽

Splitting Method ◽

Uniformly Convex ◽

Inclusion Problems ◽

Uniformly Smooth ◽

Mann Algorithm ◽

Uniformly Smooth Banach Spaces

In this paper, we give a general inertial Krasnoselskii–Mann algorithm for solving inclusion problems in Banach Spaces. First, we establish a weak convergence in real uniformly convex and q-uniformly smooth Banach spaces for finding fixed points of nonexpansive mappings. Then, a strong convergence is obtained for the inertial generalized forward-backward splitting method for the inclusion. Our results extend many recent and related results obtained in real Hilbert spaces.

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A steepest-descent Krasnosel’skii–Mann algorithm for a class of variational inequalities in Banach spaces

Journal of Fixed Point Theory and Applications ◽

10.1007/s11784-016-0290-3 ◽

2016 ◽

Vol 18 (3) ◽

pp. 519-532 ◽

Cited By ~ 7

Author(s):

Nguyen Buong ◽

Vu Xuan Quynh ◽

Nguyen Thi Thu Thuy

Keyword(s):

Variational Inequalities ◽

Banach Spaces ◽

Steepest Descent ◽

Mann Algorithm

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Relaxation of Some Confusions about Confounders

Entropy ◽

10.3390/e23111450 ◽

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.

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A Modified Krasnosel’skiǐ–Mann Iterative Algorithm for Approximating Fixed Points of Enriched Nonexpansive Mappings

Symmetry ◽

10.3390/sym14010123 ◽

2022 ◽

Vol 14 (1) ◽

pp. 123

Author(s):

Vasile Berinde

Keyword(s):

Fixed Point ◽

Strong Convergence ◽

Fixed Points ◽

Hilbert Spaces ◽

Convergence Theorem ◽

Numerical Experiments ◽

Nonexpansive Mappings ◽

Strong Convergence Theorem ◽

Fixed Point Algorithm ◽

Mann Algorithm

For approximating the fixed points of enriched nonexpansive mappings in Hilbert spaces, we consider a modified Krasnosel’skiǐ–Mann algorithm for which we prove a strong convergence theorem. We also empirically compare the rate of convergence of the modified Krasnosel’skiǐ–Mann algorithm and of the simple Krasnosel’skiǐ fixed point algorithm. Based on the numerical experiments reported in the paper we conclude that, for the class of enriched nonexpansive mappings, it is more convenient to work with the simple Krasnosel’skiǐ fixed point algorithm than with the modified Krasnosel’skiǐ–Mann algorithm.

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

Axioms ◽

10.3390/axioms11010021 ◽

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.

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