Hicks’ contraction principle

2001 ◽  
pp. 185-203
Author(s):  
Olga Hadžić ◽  
Endre Pap
Keyword(s):  
Contraction Principle

A note on the L-fuzzy Banach’s contraction principle

2009 ◽  
Vol 41 (5) ◽  
pp. 2399-2400 ◽  
Author(s):  
J. Martínez-Moreno ◽  
A. Roldán ◽  
C. Roldán
Keyword(s):  
Contraction Principle ◽  
Banach’S Contraction Principle

scholarly journals Convergence analysis of gradient-based iterative algorithms for a class of rectangular Sylvester matrix equations based on Banach contraction principle

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Adisorn Kittisopaporn ◽  
Pattrawut Chansangiam ◽  
Wicharn Lewkeeratiyutkul
Keyword(s):  
Spectral Radius ◽  
Matrix Equation ◽  
Iterative Algorithms ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Convergence Factor ◽  
Sylvester Matrix ◽  
Iteration Matrix ◽  
Banach Contraction ◽  
The Matrix

AbstractWe derive an iterative procedure for solving a generalized Sylvester matrix equation $AXB+CXD = E$ A X B + C X D = E , where $A,B,C,D,E$ A , B , C , D , E are conforming rectangular matrices. Our algorithm is based on gradients and hierarchical identification principle. We convert the matrix iteration process to a first-order linear difference vector equation with matrix coefficient. The Banach contraction principle reveals that the sequence of approximated solutions converges to the exact solution for any initial matrix if and only if the convergence factor belongs to an open interval. The contraction principle also gives the convergence rate and the error analysis, governed by the spectral radius of the associated iteration matrix. We obtain the fastest convergence factor so that the spectral radius of the iteration matrix is minimized. In particular, we obtain iterative algorithms for the matrix equation $AXB=C$ A X B = C , the Sylvester equation, and the Kalman–Yakubovich equation. We give numerical experiments of the proposed algorithm to illustrate its applicability, effectiveness, and efficiency.

Fuzzy double controlled metric spaces and related results

2021 ◽  
Vol 40 (5) ◽  
pp. 9977-9985
Author(s):  
Naeem Saleem ◽  
Hüseyin Işık ◽  
Salman Furqan ◽  
Choonkil Park
Keyword(s):  
Integral Equation ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Uniqueness Of Solution ◽  
Contraction Principle ◽  
Triangular Inequality ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we introduce the concept of fuzzy double controlled metric space that can be regarded as the generalization of fuzzy b-metric space, extended fuzzy b-metric space and controlled fuzzy metric space. We use two non-comparable functions α and β in the triangular inequality as: M q ( x , z , t α ( x , y ) + s β ( y , z ) ) ≥ M q ( x , y , t ) ∗ M q ( y , z , s ) . We prove Banach contraction principle in fuzzy double controlled metric space and generalize the Banach contraction principle in aforementioned spaces. We give some examples to support our main results. An application to existence and uniqueness of solution for an integral equation is also presented in this work.

Comments and Correction on ”U-Processes and Preference Learning” (Neural Computation Vol. 26, pp. 2896–2924, 2014)

2015 ◽  
Vol 27 (7) ◽  
pp. 1549-1553
Author(s):  
Wojciech Rejchel ◽  
Hong Li ◽  
Chuanbao Ren ◽  
Luoqing Li
Keyword(s):  
Neural Computation ◽  
Contraction Principle ◽  
Preference Learning

This note corrects an error in the proof of corollary 1 of Li et al. ( 2014 ). The original claim of the contraction principle in appendix D of Li et al. no longer holds.

Relation-theoretic contraction principle

2015 ◽  
Vol 17 (4) ◽  
pp. 693-702 ◽  
Author(s):  
Aftab Alam ◽  
Mohammad Imdad
Keyword(s):  
Contraction Principle

Some variants of Ćirić’s multi-valued contraction principle

2019 ◽  
Vol 57 (1) ◽  
pp. 23-42
Author(s):  
Cristian Daniel Alecsa ◽  
Adrian Petruşel
Keyword(s):  
Fixed Point ◽  
Fixed Point Problem ◽  
Contraction Principle ◽  
Point Problem ◽  
Strict Fixed Point ◽  
Fixed Point Principle

Abstract In this article, a study of the fixed point problem for Ćirić type multi-valued operators is presented. More precisely, some variants ofĆirić’s contraction principle for multi-valued operators, as well as a strict fixed point principle forĆirić type multi-valued will be given.

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