Generalized projections, decompositions, and the Pythagorean-type theorem in Banach spaces

DOI10.1016/S0893-9659(98)00112-8zbMath0947.46012OpenAlexW2081107090WikidataQ114120812 ScholiaQ114120812MaRDI QIDQ1808593

Ya. I. Al'ber

Publication date: 31 October 2000

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0893-9659(98)00112-8

zbMATH Keywords

variational principlesduality mappingLyapunov functionalsgeneralized projection operatorsYoung-Fenchel transformdual and polar conesPythagorean-type rules

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Nonsmooth analysis (49J52) Nonlinear accretive operators, dissipative operators, etc. (47H06) Geometry and structure of normed linear spaces (46B20) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10)

Related Items

The generalized decomposition theorem in Banach spaces and its applications ⋮ Orthogonally Complemented Subspaces in Banach Spaces ⋮ Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces ⋮ Orthogonally complemented subspaces in Banach spaces ⋮ Strong approximation of the solutions of a system of operator equations in Hilbert spaces ⋮ Effective Reifenberg theorems in Hilbert and Banach spaces ⋮ James orthogonality and orthogonal decompositions of Banach spaces

Cites Work

• Geometry of Banach spaces. Selected topics
• On the moduli of convexity and smoothness
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
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