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Carpathian Journal of Mathematics, ISSN 1584-2851, 1/2016, Volume 32, Issue 1, pp. 13 - 28
Journal Article
JOURNAL OF CONVEX ANALYSIS, ISSN 0944-6532, 2019, Volume 26, Issue 3, pp. 911 - 924
We show that in the framework of CAT(0) spaces, any convex combination of two mappings which are firmly nonexpansive - or which satisfy the more general... 
MATHEMATICS | proof mining | firmly nonexpansive mappings | asymptotic regularity | averaged projections | convex optimization | CONVERGENCE | CAT spaces
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 08/2013, Volume 87, pp. 102 - 115
We further study averaged and firmly nonexpansive mappings in the setting of geodesic spaces with a main focus on the asymptotic behavior of their Picard iterates... 
Geodesic space | Asymptotic regularity | Convex feasibility problem | Averaged mapping | Firmly nonexpansive mapping | Proof mining | MATHEMATICS, APPLIED | ALGORITHMS | CONTRACTIONS | MATHEMATICS | PROJECTION | SEMIGROUPS | ITERATIONS | REGULARITY | CONVERGENCE | OPERATORS | RANGE | Algorithms | Mining | Asymptotic properties | Proving | Nonlinearity | Feasibility | Mapping | Regularity
Journal Article
Set-valued and variational analysis, ISSN 1877-0541, 2011, Volume 20, Issue 1, pp. 131 - 153
The notion of a firmly nonexpansive mapping is central in fixed point theory because of attractive convergence properties for iterates and the correspondence with maximally monotone operators due to Minty... 
Banach contraction | 52A41 | Proximal map | Subdifferential operator | Mathematics | Nonexpansive mapping | Geometry | Maximally monotone operator | Rectangular | Resolvent | Secondary 26B25 | Primary 47H05 | 90C25 | Analysis | Firmly nonexpansive mapping | 47H09 | Convex function | Hilbert space | Legendre function | Paramonotone | Fixed point | MATHEMATICS, APPLIED | FITZPATRICK FUNCTIONS | EXTENSION | NONLINEAR OPERATORS | CONVERGENCE
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2011, Volume 74, Issue 13, pp. 4387 - 4391
We introduce the class of α -nonexpansive mappings in Banach spaces. This class contains the class of nonexpansive mappings and is related to the class of firmly nonexpansive mappings in Banach spaces... 
Fixed point theorem | Nonspreading mapping | Firmly nonexpansive mapping | Nonexpansive mapping | Hybrid mapping | MATHEMATICS | NONLINEAR MAPPINGS | MATHEMATICS, APPLIED | OPERATORS | Nonlinearity | Theorems | Fixed points (mathematics) | Mapping | Banach space
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2011, Volume 62, Issue 12, pp. 4656 - 4666
Journal Article
Journal of fixed point theory and applications, ISSN 1661-7746, 2015, Volume 18, Issue 2, pp. 297 - 307
In 1971, Pazy [Israel J. Math. 9 (1971), 235–240] presented a beautiful trichotomy result concerning the asymptotic behaviour of the iterates of a nonexpansive mapping... 
firmly nonexpansive mapping | Mathematical Methods in Physics | Secondary 90C25 | Cosmic convergence | projection operator | Analysis | Primary 47H09 | Mathematics, general | nonexpansive mapping | Mathematics | Poincaré metric | MATHEMATICS, APPLIED | ALGORITHM | ACCRETIVE-OPERATORS | Poincare metric | CONTRACTIONS | MATHEMATICS | SEMIGROUPS | MAPS | SETS | HILBERT-SPACE | RANGE | Computer science | Resveratrol
Journal Article
SIAM journal on optimization, ISSN 1095-7189, 2015, Volume 25, Issue 2, pp. 1064 - 1082
Journal Article
Mathematical Communications, ISSN 1331-0623, 06/2011, Volume 16, Issue 1, pp. 251 - 264
In this paper, two examples of quasi-firmly type nonexpansive mappings are given to prove that the concept is different from nonexpansive mapping... 
Krasnosel- skii-mann iteration | Ishikawa-type iteration | Quasi-firmly type nonexpansive mappings | MATHEMATICS | ITERATIVE PROCESS | MATHEMATICS, APPLIED | quasi-firmly type nonexpansive mappings | BANACH-SPACES | SETS | Krasnoselskii-Mann iteration | WEAK CONVERGENCE | KRASNOSELSKI | FIXED-POINTS
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2007, Volume 135, Issue 1, pp. 135 - 139
.... In the same spirit, we provide a new proof of an extension result for firmly nonexpansive mappings with an optimally localized range. 
Hilbert spaces | Mathematical functions | Mathematical duality | Mathematical theorems | Banach space | Fenchel duality | Kirszbraun-Valentine theorem | Fitzpatrick function | Firmly nonexpansive mapping | firmly nonexpansive mapping | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | fenchel duality
Journal Article
Journal of Nonlinear and Convex Analysis, ISSN 1345-4773, 01/2014, Volume 15, Issue 1, pp. 61 - 87
Journal Article
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