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Fixed points and coupled fixed points in $b$-metric spaces via graphical contractions
Carpathian Journal of Mathematics, 2022"In this paper some existence and stability results for cyclic graphical contractions in complete metric spaces are given. An application to a coupled fixed point problem is also derived."
MONICA-FELICIA BOTA +2 more
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Fixed points vs. coupled fixed points
Journal of Fixed Point Theory and Applications, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A variational principle, fixed points and coupled fixed points on $$\mathbb {P}$$ sets
Journal of Fixed Point Theory and ApplicationszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Georgiev, Valentin +2 more
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Bifurcation of Fixed Points in Coupled Josephson Junctions
SIAM Journal on Mathematical Analysis, 1996The paper deals with the investigation of fixed points of the system \(\varphi_1''+ \gamma\varphi_1'+ \sin\varphi_1+ k(\varphi_1-\varphi_2+H)=I\), \(\varphi_2''+ \gamma\varphi_2'+ \sin\varphi_2- k(\varphi_1-\varphi_2+H)=0\), which describes a pair of coupled Josephson junctions. Here \(\gamma\), \(k\), \(H\), \(I\) are constants with \(\gamma\) and \(k\
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COUPLED FIXED POINTS OF SKEW INCREASING OPERATORS AND APPLICATIONS
Acta Mathematica Scientia, 1999Let \(X\) be a Banach space with a partial ordering introduced by a cone \(K\) and let \(X_1, X_2\) be subspaces of \(X\) such that \(X_1\cup X_2= X\), \(X_1\cap X_2= \{0\}\). If \(F:X\to X\) is an operator in \(X\) then denote by \(F_i\) the term \(\pi_i\circ F\) (where \(\pi_i\) are the projections on \(X_i\)) for \(i\in \{1,2\}\).
Liu, Weian, Yang, Yin, Chen, Hua
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ON COUPLED FIXED POINTS OF \alpha-\psi-CONTRACTIVE MULTIFUNCTIONS
JP Journal of Fixed Point Theory and Applications, 2015Summary: The aim of this paper is to extend coupled fixed points of \(\alpha\)-\(\psi\)-contractive mappings to a-y-contractive multifunctions. Some examples are given to illustrate the result. The obtained result guaranties the existence of coupled fixed points of multifunctions on ordered metric spaces and contractive multifunctions.
Mohammadi, B., Alizadeh, E.
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RELATION-THEORETIC COUPLED FIXED POINT THEOREMS
Journal of Mathematical Analysis, 2022In this paper, we introduce mixed R-monotone property of a mapping and utilize the same to investigate existence and uniqueness of coupled fixed points in a metric space endowed with a binary relation R. Moreover, we present some coupled fixed point results for mappings without mixed monotone property using relation-theoretic approach.
FARUK Sk +2 more
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A variational principle and coupled fixed points
Journal of Fixed Point Theory and Applications, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Newton-Coupling of Fixed Point Iterations
1995To solve a coupled system of two equations it may be intended not to use the Newton-Raphson method, for example due to the non-sparsity of the Jacobian of the entire system or because there exist solvers for the subsystems. For this type of problems we present an iterative Newton type method which requires only iterative solution steps for the single ...
Stefan Artlich, Wolfgang Mackens
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Coupled fixed points of nonlinear operators with applications
Nonlinear Analysis: Theory, Methods & Applications, 1987Let \(D\) be a subset of a real Banach space \(E\), which is partially ordered by a cone \(P\) of \(E\). The operator \(A: D\times D\to E\) is mixed monotone if \(A(x,y)\) is nondecreasing in \(x\) and nonincreasing in \(x\). The point \((x',y')\) in \(D\times D\) is a coupled fixed point of \(A\) if \(A(x',y')=x'\) and \(A(y',x')=y'\).
Guo, Dajun, Lakshmikantham, V.
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