Applications of the Best Approximation Operator to *-Nonexpansive Maps in Hilbert Spaces

DOI10.1081/NFA-120022926zbMath1221.41019OpenAlexW2080034334MaRDI QIDQ4412386

Abdul Rahim Khan, Nawab Hussain

Publication date: 14 July 2003

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/nfa-120022926

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (17)

On solving split equilibrium problems and fixed point problems of nonspreading multi-valued mappings in Hilbert spaces ⋮ Common fixed points for multimaps in metric spaces ⋮ Iterative methods for a generalized equilibrium problem and a nonexpansive multi-valued mapping ⋮ Unnamed Item ⋮ Hybrid methods for a mixed equilibrium problem and fixed points of a countable family of multivalued nonexpansive mappings ⋮ Some new results on fixed and best proximity points in preordered metric spaces ⋮ Unnamed Item ⋮ Convergence and Data Dependency of Normal−S Iterative Method for Discontinuous Operators on Banach Space ⋮ Viscosity approximation methods for nonexpansive multi-valued nonself mappings and equilibrium problems ⋮ Best proximity point results for generalized contractions in metric spaces ⋮ Some generalizations of Ky Fan’s best approximation theorem ⋮ Approximation of common fixed points of two quasi-nonexpansive multi-valued maps in Banach spaces ⋮ Best proximity point results for modified Suzuki \(\alpha\)-\(\psi\)-proximal contractions ⋮ An implicit iteration process for solving a fixed point problem of a finite family of multi-valued mappings in Banach spaces ⋮ Coincidences of Lipschitz-Type Hybrid Maps and Invariant Approximation ⋮ Some results on the approximation of solutions of variational inequalities for multivalued maps on Banach spaces ⋮ Best proximity point results for modified \(\alpha\)-\(\psi\)-proximal rational contractions

Cites Work

• Proximity maps and fixed points
• Applications of the proximity map to fixed point theorems in Hilbert space
• Fixed points of multivalued nonexpansive maps
• Construction of fixed points of nonlinear mappings in Hilbert space
• Extensions of two fixed point theorems of F. E. Browder
• Fixed point theorems for multivalued mappings in Banach spaces
• Strong convergence theorems for nonexpansive nonself-mappings
• FIXED-POINT THEOREMS FOR NONCOMPACT MAPPINGS IN HILBERT SPACE

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