Best approximation and fixed points for rational-type contraction mappings

• Autorzy: Chandok, Sumit
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

PL

zbiór zwarty; zbiór wypukły; zbiór gwiaździsty; najlepsza aproksymacja

EN

compact sets; convex set; starshaped set; best approximation

• Czasopismo: Journal of Applied Analysis
• Rocznik: 2019
• Tom: Vol. 25, nr 2
• Strony: 205--209
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Chandok, Sumit

• 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.

Identyfikatory

DOI

10.1515/jaa-2019-0021