Common fixed points versus invariant approximation for noncommutative mappings

Hemant Kumar Nashine

doi:10.33993/jnaat371-878

Authors

Hemant Kumar Nashine Disha Institute of Management and Technology, India

DOI:

https://doi.org/10.33993/jnaat371-878

Keywords:

best approximant, common fixed points, commutating mappings, compatible mapping, demiclosed mapping, locally convex space

Abstract views: 198

Abstract

The aim of this paper is to obtain common fixed points as invariant approximation for noncommuting two pairs of mappings. As consequences, our works generalize the recent works of Nashine [9] by weakening commutativity hypothesis and by increasing the number of mappings involved.

Downloads

Download data is not yet available.

References

Brosowski, B., Fix punktsatze in der approximations theorie, Mathematica, 11, pp. 165-220, 1969.

Carbone, A., Some results on invariant approximation, Internat. J. Math. Math. Soc., 17, no. 3, pp. 483-488, 1994, https://doi.org/10.1155/s0161171294000712 DOI: https://doi.org/10.1155/S0161171294000712

Hicks, T.L. and Humpheries, M.D., A note on fixed point theorems, J. Approx. Theory, 34, pp. 221-225, 1982, https://doi.org/10.1016/0021-9045(82)90012-0 DOI: https://doi.org/10.1016/0021-9045(82)90012-0

Jungck, G., Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 9, no. 4, pp. 771-779, 1986, https://doi.org/10.1155/s0161171286000935 DOI: https://doi.org/10.1155/S0161171286000935

Jungck, G., Compactible mappings and common fixed points (2), Internat. J. Math. Math. Sci., 11, no. 2, pp. 285-288, 1988, https://doi.org/10.1155/s0161171288000341 DOI: https://doi.org/10.1155/S0161171288000341

Jungck, G. and Sessa, S., Fixed point theorems in best approximation theory, Math. Japonica., 42, no. 2, pp. 249-252, 1995.

Köthe, G., Topological vector spaces I, Die Grundlehren der mathematischen Wissenschaften, Vol. 159, Springer-Verlag, New York, 1969, https://doi.org/10.1007/978-3-642-64988-2 DOI: https://doi.org/10.1007/978-3-642-64988-2

Meinardus, G., Invarianze bei Linearen Approximationen, Arch. Rational Mech. Anal., 14, pp. 301-303, 1963, https://doi.org/10.1007/bf00250708 DOI: https://doi.org/10.1007/BF00250708

Nashine, H.K., Existence of best approximation result in locally convex space, Kungpook Math. J., 46, no. 3, pp. 389-397, 2006.

Sahab, S.A., Khan, M.S. and Sessa, S., A result in best approximation theory, J. Approx. Theory, 55, pp. 349-351, 1988, https://doi.org/10.1016/0021-9045(88)90101-3 DOI: https://doi.org/10.1016/0021-9045(88)90101-3

Singh, S.P., An application of a fixed point theorem to approximation theory, J. Approx. Theory, 25, pp. 89-90, 1979, https://doi.org/10.1016/0021-9045(79)90036-4 DOI: https://doi.org/10.1016/0021-9045(79)90036-4

Singh, S.P., Application of fixed point theorems to approximation theory, in: V. Lakshmikantam (Ed.), Applied Nonlinear Analysis, Academic Press, New York, 1979, https://doi.org/10.1016/b978-0-12-434180-7.50038-3 ?? https://doi.org/10.1016/0021-9045(79)90036-4 DOI: https://doi.org/10.1016/B978-0-12-434180-7.50038-3

Singh, S.P., Some results on best approximation in locally convex spaces, J. Approx. Theory, 28, pp. 329-332, 1980, https://doi.org/10.1016/0021-9045(80)90067-2 DOI: https://doi.org/10.1016/0021-9045(80)90067-2

Subrahmanyam, P.V., An application of a fixed point theorem to best approximations, J. Approx. Theory, 20, pp. 165-172, 1977, https://doi.org/10.1016/0021-9045(77)90070-3 DOI: https://doi.org/10.1016/0021-9045(77)90070-3

Tarafdar, E., Some fixed point theorems on locally convex linear topological spaces, Bull. Austral. Math. Soc., 13, pp. 241-254, 1975, https://doi.org/10.1017/s0004972700024436 DOI: https://doi.org/10.1017/S0004972700024436