Best approximation and fixed points for rational-type contraction mappings

References

[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. 10.1155/S0161171202007524Search in Google Scholar

[2] B. Brosowski, Fixpunktsätze in der Approximationstheorie, Mathematica (Cluj) 11(34) (1969), 195–220. Search in Google Scholar

[3] S. Chandok, Some common fixed point theorems for generalized nonlinear contractive mappings, Comput. Math. Appl. 62 (2011), no. 10, 3692–3699. 10.1016/j.camwa.2011.09.009Search in Google Scholar

[4] S. Chandok, Common fixed points, invariant approximation and generalized weak contractions, Int. J. Math. Math. Sci. (2012), Article ID 102980. 10.1155/2012/102980Search in Google Scholar

[5] S. Chandok, Common fixed points and invariant approximation for noncommuting asymptotic weak contractions, J. Adv. Math. Stud. 6 (2013), no. 1, 12–18. Search in Google Scholar

[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. Search in Google Scholar

[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. 10.1515/jaa-2012-0002Search in Google Scholar

[8] S. Chandok and T. D. Narang, Common fixed points with applications to best simultaneous approximations, Anal. Theory Appl. 28 (2012), 1–12. 10.4208/ata.2012.v28.n1.1Search in Google Scholar

[9] S. K. Chatterjea, Fixed-point theorems, C. R. Acad. Bulgare Sci. 25 (1972), 727–730. 10.1501/Commua1_0000000548Search in Google Scholar

[10] B. Fisher, A fixed-point theorem for compact metric spaces, Publ. Math. Debrecen 25 (1978), no. 3–4, 193–194. 10.5486/PMD.1978.25.3-4.01Search in Google Scholar

[11] C. Franchetti and M. Furi, Some characteristic properties of real Hilbert spaces, Rev. Roumaine Math. Pures. Appl. 17 (1972), 1045–1048. Search in Google Scholar

[12] M. I. Ganzburg, Invariance theorems in approximation theory and their applications, Constr. Approx. 27 (2008), no. 3, 289–321. 10.1007/s00365-006-0670-3Search in Google Scholar

[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. 10.1007/BF01085888Search in Google Scholar

[14] D. S. Jaggi, Some unique fixed point theorems, Indian J. Pure Appl. Math. 8 (1977), no. 2, 223–230. Search in Google Scholar

[15] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60 (1968), 71–76. Search in Google Scholar

[16] G. Meinardus, Invarianz bei linearen Approximationen, Arch. Ration. Mech. Anal. 14 (1963), 301–303. 10.1007/BF00250708Search in Google Scholar

[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. Search in Google Scholar

[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. Search in Google Scholar

[19] T. D. Narang, On best coapproximation in normed linear spaces, Rocky Mountain J. Math. 22 (1992), no. 1, 265–287. 10.1216/rmjm/1181072810Search in Google Scholar

[20] T. D. Narang and S. Chandok, Fixed points and best approximation in metric spaces, Indian J. Math. 51 (2009), no. 2, 293–303. Search in Google Scholar

[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. Search in Google Scholar

[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. Search in Google Scholar

[23] G. S. Rao and S. A. Mariadoss, Applications of fixed point theorems to best approximations, Serdica 9 (1983), no. 3, 244–248. Search in Google Scholar

[24] S. Reich, Some remarks concerning contraction mappings, Canad. Math. Bull. 14 (1971), 121–124. 10.4153/CMB-1971-024-9Search in Google Scholar

[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. 10.1007/978-3-662-41583-2Search in Google Scholar

[26] S. P. Singh, An application of a fixed-point theorem to approximation theory, J. Approx. Theory 25 (1979), no. 1, 89–90. 10.1016/0021-9045(79)90036-4Search in Google Scholar

[27] S. P. Singh, Application of fixed point theorems in approximation theory, Applied Nonlinear Analyis, Academic Press, New York (1979), 389–397. 10.1016/B978-0-12-434180-7.50038-3Search in Google Scholar