Fixed point results satisfying rational type contractive conditions in complex valued metric spaces



Abstract

The aim of this manuscript is to establish fixed point results satisfying contractive conditions of rational type in the setting of complex valued metric spaces. The derived results generalize and extend some well known results in the existing literature.


Keywords

complex valued metric spaces; common fixed points; self-maps; Cauchy sequence; contractive conditions

1. Azam A., Fisher B., Khan M., Common fixed point theorems in complex valued metric spaces, Numer. Funct. Anal. Optim. 32 (2011), no. 3, 243–253.
2. Banach S., Sur les opérations dans les ensembles abstraits et leurs applications aux equations integrales, Fund. Math. 3 (1922), 133–181.
3. Klin-eam C., Suanoom C., Some common fixed point theorems for generalized contractive type mappings on complex valued metric spaces, Abstr. Appl. Anal. 2013, Art. ID 604215, 6 pp.
4. Kumar T.S., Hussain R.J., Common fixed point theorems in complex valued metric spaces, Int. J. Innov. Res. Sci. Engrg. 2 (2014), no. 14, 834–838.
5. Rouzkard F., Imdad M., Some common fixed point theorems on complex valued metric spaces, Comput. Math. Appl. 64 (2012), no. 6, 1866–1874.
6. Sitthikul K., Saejung S., Some fixed point theorems in complex valued metric space, Fixed Point Theory Appl. 2012, 189, 11 pp.
7. Sintunavarat W., Kumam P., Common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space, J. Appl. Math. 2011, Art. ID 637958, 14 pp.
8. Sintunavarat W., Kumam P., Generalized common fixed point theorems in complex valued metric spaces and applications, J. Inequal. Appl. 2012, 84, 12 pp.
Download

Published : 2016-09-23


KumamP., SarwarM., & ZadaM. B. (2016). Fixed point results satisfying rational type contractive conditions in complex valued metric spaces. Annales Mathematicae Silesianae, 30, 89-110. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13958

Poom Kumam  poom.kum@kmutt.ac.th
Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Thailand  Thailand
Muhammad Sarwar 
Department of Mathematics, University of Malakand, Pakistan  Pakistan
Mian Bahadur Zada 
Department of Mathematics, University of Malakand, Pakistan  Pakistan



Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.

  1. License
    This journal provides immediate open access to its content under the Creative Commons BY 4.0 license (http://creativecommons.org/licenses/by/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY 4.0 license.
  2. Author’s Warranties
    The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s.
  3. User Rights
    Under the Creative Commons Attribution license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor.
  4. Co-Authorship
    If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.