Linear and continuous operators on Hilbert spaces

2003 ◽  
pp. 305-365
Author(s):  
Constantin Costara ◽  
Dumitru Popa
Keyword(s):  
Hilbert Spaces ◽  
Continuous Operators

scholarly journals Projected Subgradient Algorithms for Pseudomonotone Equilibrium Problems and Fixed Points of Pseudocontractive Operators

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 461 ◽  
Author(s):  
Yonghong Yao ◽  
Naseer Shahzad ◽  
Jen-Chih Yao
Keyword(s):  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Convergence Result ◽  
Subgradient Method ◽  
Iterative Sequence ◽  
Common Element ◽  
Lipschitz Continuous ◽  
Subgradient Algorithms ◽  
Continuous Operators

The projected subgradient algorithms can be considered as an improvement of the projected algorithms and the subgradient algorithms for the equilibrium problems of the class of monotone and Lipschitz continuous operators. In this paper, we present and analyze an iterative algorithm for finding a common element of the fixed point of pseudocontractive operators and the pseudomonotone equilibrium problem in Hilbert spaces. The suggested iterative algorithm is based on the projected method and subgradient method with a linearsearch technique. We show the strong convergence result for the iterative sequence generated by this algorithm. Some applications are also included. Our result improves and extends some existing results in the literature.

scholarly journals Inertial S-type Tseng's extragradient Algorithm for solution of Variational Inequality problems

2021 ◽  
Author(s):  
D. R. Sahu ◽  
AMIT KUMAR SINGH
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Iteration Process ◽  
Variational Inequality Problems ◽  
Numerical Examples ◽  
Lipschitz Continuous ◽  
Mild Conditions ◽  
Extragradient Algorithm ◽  
Convergence Results ◽  
Continuous Operators

In this paper, we introduce inertial Tseng’s extragradient algorithms combined with normal-S iteration process for solving variational inequality problems involving pseudo-monotone and Lipschitz continuous operators. Under mild conditions, we establish the weak convergence results in Hilbert spaces. Numerical examples are also present to show that faster behaviour of the proposed method.

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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