Title: Fixed Point Theorem of Ciric-Pata Type
Author(s): Ao-Lei Sima, Fei He, Ning Lu
Pages: 275-281
Cite as:
Ao-Lei Sima, Fei He, Ning Lu, Fixed Point Theorem of Ciric-Pata Type, Int. J. Anal. Appl., 17 (2) (2019), 275-281.


In this article, we proved a fixed point theorem of Ćirić-Pata type in metric space. This result extends several results in the existing literature. Moreover, an example is given in the support of our result. In particular, the main result provides a complete solution to an open problem raised by Kadelburg and Radenović (J. Egypt. Math. Soc. 24 (2016) 77-82).

Full Text: PDF



  1. V. Pata, A fixed point theorems in metric spaces, J. Fixed Point Theory Appl. 10 (2011), 299–305. Google Scholar

  2. M. A. Alghamdi, A. Petrusel and N. Shahzad, Correction: A fixed point theorem for cyclic generalized contractions in metric spaces, Fixed Point Theory Appl. 2012 (2012), 122. Google Scholar

  3. S. Balasubramanian, A Pata-type fixed point theorem, Math. Sci. 8 (2014), 65–69. Google Scholar

  4. M. Eshaghi, S. Mohseni, M. R. Delavar, M. De La Sen, G. H. Kim and A. Arian, Pata contractions and coupled type fixed points, Fixed Point Theory Appl. 2014 (2014), 130. Google Scholar

  5. G. K. Jacob, M. S. Khan, C. Park and S. Jun, On generalized Pata type contractions, Mathmatics. 6 (2018), 25. Google Scholar

  6. Z. Kadelburg and S. Radenović, Fixed point and tripled fixed point theorems under Pata-type conditions in ordered metric spaces, International Journal of Analysis and Applications. 6 (2014), 113–122. Google Scholar

  7. Z. Kadelburg and S. Radenović, Fixed points theorems under Pata-type conditions in metric spaces, J. Egypt. Math. Soc. 24 (2016), 77–82. Google Scholar

  8. S. M. Kolagar, M. Ramezani and M. Eshaghi, Pata type fixed point theorems of multivalued operators in ordered metric spaces with applications to hyperbolic differential inclusions, Proc. Amer. Math. Soc. 6 (2016), 21–34. Google Scholar

  9. M. Paknazar, M. Eshaghi, Y. J. Cho and S. M. Vaezpour, A Pata-type fixed point theorem in modular spaces with application, Fixed Point Theory and Appl. 2013 (2013), 239. Google Scholar

  10. L. J. Ćirić, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc. 45 (1974), 267–273. Google Scholar