scholarly journals Generalized projection operators in Geometric Algebra

2001 ◽  
Vol 11 (2) ◽  
pp. 231-238 ◽  
Author(s):  
T. A. Bouma
Keyword(s):  
Geometric Algebra ◽  
Generalized Projection ◽  
Projection Operators ◽  
Generalized Projection Operators

scholarly journals Bregman Distance and Strong Convergence of Proximal-Type Algorithms

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Li-Wei Kuo ◽  
D. R. Sahu
Keyword(s):  
Nonexpansive Mappings ◽  
Monotone Operators ◽  
Bregman Distance ◽  
Generalized Projection ◽  
Projection Operators ◽  
Proximal Point ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Generalized Projection Operators ◽  
Firmly Nonexpansive Mappings

The purpose of this paper is to discuss some fundamental properties of Bregman distance, generalized projection operators, firmly nonexpansive mappings, and resolvent operators of set-valued monotone operators corresponding to a functionalΦ(∥·∥). We further study some proximal point algorithms for finding zeros of monotone operators and solving generalized mixed equilibrium problems in Banach spaces. Our results improve and extend some recent results concerning generalized projection operators corresponding to Bregman distance.

scholarly journals Global Dynamical Systems Involving Generalized -Projection Operators and Set-Valued Perturbation in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Yun-zhi Zou ◽  
Xi Li ◽  
Nan-jing Huang ◽  
Chang-yin Sun
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Banach Spaces ◽  
Equilibrium Points ◽  
Projection Operators ◽  
Initial Value ◽  
New Class ◽  
The Fixed Point Theorem ◽  
Generalized Projection Operators ◽  
Generalized Dynamical Systems

A new class of generalized dynamical systems involving generalizedf-projection operators is introduced and studied in Banach spaces. By using the fixed-point theorem due to Nadler, the equilibrium points set of this class of generalized global dynamical systems is proved to be nonempty and closed under some suitable conditions. Moreover, the solutions set of the systems with set-valued perturbation is showed to be continuous with respect to the initial value.

scholarly journals A proximal point method for nonsmooth convex optimization problems in Banach spaces

1997 ◽  
Vol 2 (1-2) ◽  
pp. 97-120 ◽  
Author(s):  
Y. I. Alber ◽  
R. S. Burachik ◽  
A. N. Iusem
Keyword(s):  
Banach Space ◽  
Convex Optimization ◽  
Banach Spaces ◽  
Optimization Problems ◽  
Geometric Characteristic ◽  
Point Method ◽  
Proximal Point Method ◽  
Projection Operators ◽  
Proximal Point ◽  
Generalized Projection Operators

In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the dual Banach space, namely its modulus of convexity. We apply a new technique which includes Banach space geometry, estimates of duality mappings, nonstandard Lyapunov functionals and generalized projection operators in Banach spaces.

On the Zap Integral Operators over Fourier Transforms

2021 ◽  
Author(s):  
Juan Manuel Velazquez Arcos ◽  
Ricardo Teodoro Paez Hernandez ◽  
Alejandro Perez Ricardez ◽  
Jaime Granados Samaniego ◽  
Alicia Cid Reborido
Keyword(s):  
Integral Equation ◽  
Quantum Mechanics ◽  
Fourier Transforms ◽  
Integral Operators ◽  
Integral Transforms ◽  
Fourier Integral ◽  
Fredholm Equation ◽  
Projection Operators ◽  
Inhomogeneous Term ◽  
Generalized Projection Operators

We devote the current chapter to describe a class of integral operators with properties equivalent to a killer operator of the quantum mechanics theory acting over a determined state, literally killing the state but now operating over some kind of Fourier integral transforms that satisfies a certain Fredholm integral equation, we call this operators Zap Integral Operators (ZIO). The result of this action is to eliminate the inhomogeneous term and recover a homogeneous integral equation. We show that thanks to this class of operators we can explain the presence of two extremely different solutions of the same Generalized Inhomogeneous Fredholm equation. So we can regard the Generalized Inhomogeneous Fredholm Equation as a Super-Equation with two kinds of solutions, the resonant and the conventional but coexisting simultaneously. Also, we remember the generalized projection operators and we show they are the precursors of the ZIO. We present simultaneous academic examples for both kinds of solutions.

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