Tytuł artykułu
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Abstrakty
In this paper, we prove a fixed point theorem for a rational type contraction mapping in the frame work of metric spaces. Also, we extend Brosowski-Meinardus type results on invariant approximation for such class of contraction mappings. The results proved extend some of the known results existing in the literature.
Wydawca
Czasopismo
Rocznik
Tom
Strony
205--209
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
autor
- School of Mathematics, Thapar Institute of Engineering & Technology, Patiala-147004, Punjab, India
Bibliografia
- [1] A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 29 (2002), no. 9, 531-536.
- [2] B. Brosowski, Fixpunktsätze in der Approximationstheorie, Mathematica (Cluj) 11(34) (1969), 195-220.
- [3] S. Chandok, Some common fixed point theorems for generalized nonlinear contractive mappings, Comput. Math. Appl. 62 (2011), no. 10, 3692-3699.
- [4] S. Chandok, Common fixed points, invariant approximation and generalized weak contractions, Int. J. Math. Math. Sci. (2012), Article ID 102980.
- [5] S. Chandok, Common fixed points and invariant approximation for noncommuting asymptotic weak contractions, J. Adv. Math. Stud. 6 (2013), no. 1, 12-18.
- [6] S. Chandok, J. Liang and D. O’Regan, Common fixed points and invariant approximations for noncommuting contraction mappings in strongly convex metric spaces, J. Nonlinear Convex Anal. 15 (2014), no. 6, 1113-1123.
- [7] S. Chandok and T. D. Narang, Common fixed points of nonexpansive mappings with applications to best and best simultaneous approximation, J. Appl. Anal. 18 (2012), no. 1, 33-46.
- [8] S. Chandok and T. D. Narang, Common fixed points with applications to best simultaneous approximations, Anal. Theory Appl. 28 (2012), 1-12.
- [9] S. K. Chatterjea, Fixed-point theorems, C. R. Acad. Bulgare Sci. 25 (1972), 727-730.
- [10] B. Fisher, A fixed-point theorem for compact metric spaces, Publ. Math. Debrecen 25 (1978), no. 3-4, 193-194.
- [11] C. Franchetti and M. Furi, Some characteristic properties of real Hilbert spaces, Rev. Roumaine Math. Pures. Appl. 17 (1972), 1045-1048.
- [12] M. I. Ganzburg, Invariance theorems in approximation theory and their applications, Constr. Approx. 27 (2008), no. 3, 289-321.
- [13] M. I. Ganzburg and S. A. Pichugov, Invariance of the elements of best approximation and a theorem of Glaeser, Ukrainian Math. J. 33 (1982), 508-510.
- [14] D. S. Jaggi, Some unique fixed point theorems, Indian J. Pure Appl. Math. 8 (1977), no. 2, 223-230.
- [15] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60 (1968), 71-76.
- [16] G. Meinardus, Invarianz bei linearen Approximationen, Arch. Ration. Mech. Anal. 14 (1963), 301-303.
- [17] R. N. Mukherjee and T. Som, A note on an application of a fixed point theorem in approximation theory, Indian J. Pure Appl. Math. 16 (1985), no. 3, 243-244.
- [18] R. N. Mukherjee and V. Varma, Best approximations and fixed points of nonexpansive maps, Bull. Calcutta Math. Soc. 81 (1989), no. 3, 191-196.
- [19] T. D. Narang, On best coapproximation in normed linear spaces, Rocky Mountain J. Math. 22 (1992), no. 1, 265-287.
- [20] T. D. Narang and S. Chandok, Fixed points and best approximation in metric spaces, Indian J. Math. 51 (2009), no. 2, 293-303.
- [21] T. D. Narang and S. Chandok, Fixed points of quasi-nonexpansive mappings and best approximation, Selçuk J. Appl. Math. 10 (2009), no. 2, 75-80.
- [22] T. D. Narang and S. Chandok, On ϵ-approximation and fixed points of nonexpansive mappings in metric spaces, Mat. Vesnik 61 (2009), no. 2, 165-171.
- [23] G. S. Rao and S. A. Mariadoss, Applications of fixed point theorems to best approximations, Serdica 9 (1983), no. 3, 244-248.
- [24] S. Reich, Some remarks concerning contraction mappings, Canad. Math. Bull. 14 (1971), 121-124.
- [25] I. Singer, Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces. Translated from the Romanian by Radu Georgescu, Grundlehren Math. Wiss. 171, Springer, Berlin, 1970.
- [26] S. P. Singh, An application of a fixed-point theorem to approximation theory, J. Approx. Theory 25 (1979), no. 1, 89-90.
- [27] S. P. Singh, Application of fixed point theorems in approximation theory, in: Applied Nonlinear Analyis, Academic Press, New York (1979), 389-397.
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Bibliografia
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