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BY-NC-ND 3.0 license Open Access Published by De Gruyter May 8, 2014

Fixed points for mappings with a contractive iterate at each point

  • Samet Karaibryamov EMAIL logo and Boyan Zlatanov
From the journal Mathematica Slovaca

Abstract

We generalize the results of Sehgal and Guseman for mappings on a complete metric space with a contractive iterate condition at each point.

[1] BANACH, S.: Sur les opérations dan les ensembles abstraits et leurs applications aux integrales, Fund. Math. 3 (1922), 133–181. 10.4064/fm-3-1-133-181Search in Google Scholar

[2] ĆIRIĆ, L.: Fixed point theorems for mappings with a generalized contractive at a point. Publ. Inst. Math. (N.S) 13 (1972), 11–16. Search in Google Scholar

[3] ĆIRIĆ, L.: On Sehgal’s maps with a contractive iterate at a point, Publ. Inst. Math. (N.S) 33(47) (1983), 59–62. Search in Google Scholar

[4] GAJIRĆ, L.— LOZANOV-CRVENKOVIRĆ, Z.: On Mappings with Contractive Iterate at a Point in Generalized Metric Spaces, Fixed Point Theory Appl. 1000, Article ID 458086, 16 pp. 10.1155/2010/458086Search in Google Scholar

[5] GAJIRĆ, L.— LOZANOV-CRVENKOVIRĆ, Z.: On Mappings with contractive iterate at a point in G-metric spaces, Filomat 25 (2011), No. 2, 53–58, http://www.pmf.ni.ac.rs/filomat http://dx.doi.org/10.2298/FIL1102053G10.2298/FIL1102053GSearch in Google Scholar

[6] MATKOWSKIW, J.: Fixed points theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc. 62 (1977), 344–348. http://dx.doi.org/10.1090/S0002-9939-1977-0436113-510.1090/S0002-9939-1977-0436113-5Search in Google Scholar

[7] GUSEMAN, L.: Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc. 26 (1970), 615–618. http://dx.doi.org/10.1090/S0002-9939-1970-0266010-310.1090/S0002-9939-1970-0266010-3Search in Google Scholar

[8] SEHGAL, V.: A fixed point theorem for mappings with a contractive iterate, Proc. Amer. Math. Soc. 23 (1969), 631–634. http://dx.doi.org/10.1090/S0002-9939-1969-0250292-X10.1090/S0002-9939-1969-0250292-XSearch in Google Scholar

Published Online: 2014-5-8
Published in Print: 2014-4-1

© 2014 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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