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In this paper we generalize and extend Brosowski-Meinardus type results on invariant points from the set of best approximation to the set of best simultaneous approximation, which is not necessarily starshaped. As a consequence some results on best approximation are deduced. The proved results extend and generalize some of the results of R. N. Mukherjee and V. Verma [Publ. de l’Inst. Math. 49(1991) 111-116], T.D. Narang and S. Chandok [Selcuk J. Appl. Math. 10(2009) 75-80; Indian J. Math. 51(2009) 293-303], and of G. S. Rao and S. A. Mariadoss [Serdica-Bulgaricae Math. Publ. 9(1983) 244-248].
Czasopismo
Rocznik
Tom
Strony
61--70
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
- Department of Mathematics Khalsa College of Engineering & Technology Punjab Technical University Ranjit Avenue, Amritsar-143001, Punjab, India
autor
- Department of Mathematics Guru Nanak Dev University Amritsar-143005, India
Bibliografia
- [1] Bose R.K., Mukherjee R.N., Stability of fixed point sets and common fixed points of famililes of mappings, Indian J. Pure Appl. Math., 11(1980), 1130-1138.
- [2] Brosowski B., Fixpunktsatze in der approximations theorie, Mathematica (Cluj), 11(1969), 195-220.
- [3] Chandok S., Narang T.D., Common fixed points with applications to best simultaneous approximations, Anal. Theory Appl., 28(1)(2012), 1-12.
- [4] Chandok S., Narang T.D., Common fixed points of nonexpansive mappings with applications to best and best simultaneous approximation, J. Appl. Anal., 18(1)(2012), 33-46 doi:10.1515/jaa-2012-0002.
- [5] Dotson W.G., On fixed points of nonexpansive mappings in nonconvex sets, Proc. Amer. Math. Soc., 38(1973), 155-156.
- [6] Guay M.D., Singh K.L., Whitfield J.H.M., Fixed point theorems for nonexpansive mappings in convex metric spaces, Proc. Conference on nonlinear analysis (Ed. S.P. Singh and J.H. Bury) Marcel Dekker, 80(1982), 179-189.
- [7] Hardy G.E., Rogers T.D., A generalization of a fixed point theorem of Reich, Canad. Math. Bull., 16(1973), 201-206.
- [8] Iseki K., On common fixed points of mappings, Bull. Austr. Math. Soc., 10(1975), 365-370.
- [9] Itoh S., Some fixed point theorems in metric spaces, Fundamenta Mathematicae, 52(1979), 109-117.
- [10] Joshi M.C., Bose R.K., Some Topics in Nonlinear Functional Analysis, Wiley Eastern, New Delhi, 1985.
- [11] Meinardus G., Invarianz bei linearen approximationen, Arch. Rational Mach. Anal., 14(1963), 301-303.
- [12] Mukherjee R.N., Som T., A note on application of a fixed point theorem in approximation theory, Indian J. Pure Appl. Math., 16(1985), 243-244.
- [13] Mukherjee R.N., Verma V., Some fixed point theorems and their applications to best simultaneous approximations, Publ. de l’Inst. Math., 49(1991), 111-116.
- [14] Narang T.D., Chandok S., Fixed points of quasi-nonexpansive mappings and best approximation, Selęuk J. Appl. Math., 10(2009), 75-80.
- [15] Narang T.D., Chandok S., Fixed points and best approximation in metric spaces, Indian J. Math., 51(2009), 293-303.
- [16] Narang T.D., Chandok S., Some fixed point theorems with applications to best simultaneous approximation, J. Nonlinear Sci. Appl., 3(2010), 87-95.
- [17] Rao G.S., Mariadoss S.A., Applications of fixed point theorems to best approximations, Serdica-Bulgaricae Math. Publ., 9(1983), 244-248.
- [18] Sahab S.A., Khan M.S., Some results on best approximation, Review of Research, 17(1987), 143-152.
- [19] Singh S.P., An application of a fixed-point theorem to approximation theory, J. Approx. Theory, 25(1979), 89-90.
- [20] Singh S.P., Application of fixed point theorems in approximation theory, Appl. Nonlinear Anal.(Ed. V. Lakshmikantham), Academic Press, New York, 1979, 389-397.
- [21] Singh S., Watson B., Srivastava P., Fixed Point Theory and Best Approx- imation: The KKM-map Principle, Kluwer Academic Publishers, Dordrecht, 1997.
- [22] Singer i., Best Apprroximation in Normed Linear Spaces by Elements of Linear Subspaces, Springer-Verlag, New York, 1970.
- [23] Takahashi W., A convexity in metric space and nonexpansive mappings I, Kodai Math. Sem. Rep., 22(1970), 142-149.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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