The aim of this paper is to establish a fixed point theorem satisfying Ciric’s almost generalized contractive condition mappings with -distance in complete metric spaces. This result extends substantially some well known results. Further, we illustrate our main result by means of an example.

fixed point, complete metric space, -distance, condition (B), almost generalized contractive condition.

Received: January 20, 2021; Accepted: February 22, 2021; Published: March 9, 2021

How to cite this article: Koti N. V. V. Vara Prasad, The existence of fixed points for ciric’s almost generalized contractive condition mappings in complete metric spaces via w₀-distances, JP Journal of Fixed Point Theory and Applications 16(1) (2021), 19-32. DOI: 10.17654/FP016010019

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] G. V. R. Babu, M. L. Sandhya and M. V. R. Kameswari, A note on fixed point theorem of Berinde on weak contractions, Carpathian J. Math. 24(1) (2008), 8-12.
[2] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux- equations integrales, Fund. Math. 3 (1922), 133-181.
[3] V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum 9(1) (2004), 43-53.
[4] V. Berinde, General constructive fixed point theorems for Ciric-type almost contractions in metric spaces, Carpathian J. Math. 24(2) (2008), 10-19.
[5] A. Branciari, A fixed point theorem for mapping satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 10 (2002), 531-536.
[6] Lj. B. Ciric, M. Abbas, R. Saadati and N. Hussain, Common fixed points of almost generalized contractive mappings in ordered metric spaces, Appl. Math. Comput. 217 (2011), 5784-5789.
[7] O. Kada, T. Suzuki and W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Mathematica Japonica 44(2) (1996), 381-391.
[8] H. Lakzian, H. Aydi and B. E. Rhoades, Fixed points for -weakly contractive mappings in metric spaces with w-distance, Appl. Math. Comput. 219 (2013), 6777-6782.
[9] H. Lakzian and I.-J. Lin, The existence of fixed points for nonlinear contractive maps in metric spaces with w-distances, J. Appl. Math. 2012, Article ID 161470, 11 pages. doi: 10.1155/2012/161470.
[10] H. Lakzian and B. E. Rhoades, Some fixed point theorems using weaker Meir-Keeler function in metric spaces with w-distance, Appl. Math. Comput. 342 (2019), 18-25.
[11] Z. Liu, F. Hou, Shin Min Kang and Jeong Sheok Ume, On fixed point theorems for contractive mappings of integral type with w-distance, Filomat 31(6) (2017), 1515-1528. doi: 10.2298/FIL1706515L.
[12] L. J. Lin and W. S. Du, Ekeland’s variational principle, minimax theorems and existence of nonconvex equilibria in complete metric spaces, J. Math. Anal. Appl. 323 (2006), 360-370.
[13] L. J. Lin and W. S. Du, Some equivalent formulations of the generalized Ekeland’s variational principle and their applications, Nonlinear Anal. 67 (2007), 187-199.
[14] L. J. Lin and W. S. Du, On maximal element theorems, variants of Ekeland’s variational principle and their applications, Nonlinear Anal. 68 (2008), 1246-1262.
[15] K. N. V. V. Vara Prasad, A fixed point theorem on weak contraction condition (B) in complete metric spaces with w-distance, Palestine J. Math. (accepted).
[16] Wei-Shih Du, Fixed point theorems for generalized Hausdorff metrics, Int. Math. Forum 3(21) (2008), 1011-1022.