论文信息 - A fixed point theorem in partially ordered sets and some applications to matrix equations

A fixed point theorem in partially ordered sets and some applications to matrix equations

An analogue of Banach's fixed point theorem in partially ordered sets is proved in this paper, and several applications to linear and nonlinear matrix equations are discussed.

A. Ran | M. Reurings

[1] Fehmi Cirak,et al. ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND MECHANIK , 1952, Über Stammfaktoren bei ternären quadratischen Formen.

[2] A. Tarski. A LATTICE-THEORETICAL FIXPOINT THEOREM AND ITS APPLICATIONS , 1955 .

[3] H. Schneider. Positive operators and an inertia theorem , 1965 .

[4] Peter Lancaster,et al. The theory of matrices , 1969 .

[5] C. Blair,et al. An extension and simple proof of a constrained lattice fixed point theorem , 1979 .

[6] A. Björner. Order-reversing maps and unique fixed points in complete lattices , 1981 .

[7] I. Gohberg,et al. Basic Operator Theory , 1981 .

[8] F. R. Gantmakher. The Theory of Matrices , 1984 .

[9] Charles R. Johnson,et al. Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[10] Lev A. Sakhnovich,et al. Interpolation Theory and Its Applications , 1997 .

[11] André C. M. Ran,et al. On an Iteration Method for Solving a Class of Nonlinear Matrix Equations , 2001, SIAM J. Matrix Anal. Appl..

[12] A. Ran,et al. The symmetric linear matrix equation , 2002 .

[13] A. Ran,et al. A nonlinear matrix equation connected to interpolation theory , 2004 .