Two results on Jachymski-Schörder-Stein contractions

• Autorzy: Reich S. , Zaslavski A. J.
• Języki publikacji: EN

Abstrakty

EN

We establish two fixed point theorems for certain mappings of contractive type.

Słowa kluczowe

EN

complete metric space; contractive mapping; fixed point; iteration

PL

punkt stały; iteracja

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: Vol. 56, no 1
• Strony: 53--58
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Reich S.

autor

Zaslavski A. J.

• Department of Mathematics, The Technion-Israel Institute of Technology, 32000 Haifa, Israel,

Bibliografia

• [1] A. D. Arvanitakis, A proof of the generalized Banach contraction conjecture, Proc. Amer. Math. Soc. 131 (2003), 3647-3656.
• [2] D. W. Boyd and J. S. W. Wong, On nonlinear contractions, ibid. 20 (1969), 458-464.
• [3] F. E. Browder, On the convergence of successive approximations for nonlinear functional equations, Indag. Math. 30 (1968), 27-35.
• [4] D. Butnariu, S. Reich and A. J. Zaslavski, Asymptotic behavior of inexact orbits for a class of operators in complete metric spaces, J. Appl. Anal. 13 (2007), 1-11.
• [5] K. Goebel, Concise Course on Fixed Point Theorems, Yokohama Publ., Yokohama, 2002.
• [6] K. Goebel and S. Reich, Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Dekker, New York and Basel, 1984.
• [7] J. R. Jachymski, B. Schröder and J. D. Stein, Jr., A connection between fixed point theorems and tiling problems, J. Combin. Theory Ser. A 87 (1999), 273-286.
• [8] J. R. Jachymski and J. D. Stein, Jr., A minimum condition and some related fixed-point theorems, J. Austral. Math. Soc. Ser. A 66 (1999), 224-243.
• [9] J. Merryfleld, B. Rothschild and J. D. Stein, Jr., An application of Ramsey’s theorem to the Banach contraction principle, Proc. Amer. Math. Soc. 130 (2001), 927-933.
• [10] J. Merryfield and J. D. Stein, Jr., A generalization of the Banach contraction principle, J. Math. Anal. Appl. 273 (2002), 112-120.
• [11] J. D. Stein, Jr., A systematic generalization procedure for fixed-point theorems, Rocky Mountain J. Math. 30 (2000), 735-754.