Keywords:-
Article Content:-
Abstract
In this article, we obtain some fixed point results single valued mappings with rational expression in the setting of a parametric b-metric space. The presented the orems extend, generalize and improve many existing results in the literature. Also, we introduce some examples the support the validity of our results.
References:-
References
Nawab Hussain, Peyman Salimi, Vahid Parvaneh, Fixed point results for various contractions in
parametric and fuzzy b-metric spaces, J. Nonlinear Sci. Appl. 8 (2015), 719-739.R. Jain, R. D. Daheriya and M. Ughade, Fixed Point, Coincidence Point and Common Fixed Point
Theorems under Various Expansive Conditions in b-Metric Spaces, International Journal of
Scientific and Innovative Mathematical Research, vol.3, no.9, pp. 26-34, 2015.
L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338–353, 1965.
I. Kramosil and J. Michalek, “Fuzzy metrics and statistical metric spaces,” Kybernetika, vol. 11, no.
, pp. 336–344, 1975.
J. H. Park, “Intuitionistic fuzzy metric spaces,” Chaos, Solitons and Fractals, vol. 22, no. 5, pp.
–1046, 2004.
C. Alaca, D. Turkoglu, and C. Yildiz, “Fixed points in intuitionistic fuzzy metric spaces,” Chaos,
Solitons & Fractals, vol.29, no. 5, pp.1073–1078, 2006.
D. Coker, “An introduction to intuitionistic fuzzy topological spaces,” Fuzzy Sets and Systems, vol.
, no. 1, pp. 81–89, 1997.
J. S. Park, Y. C. Kwun, and J. H. Park, “A fixed point theorem in the intuitionistic fuzzy metric
spaces,” Far East Journal of Mathematical Sciences, vol. 16, no. 2, pp. 137–149, 2005.
M. Rafi and M. S. M. Noorani, “Fixed point theorem on intuitionistic fuzzy metric spaces,” Iranian
Journal of Fuzzy Systems, vol. 3, no. 1, pp. 23–29, 2006.
B. Schweizer and A. Sklar, “Statistical metric spaces,” Pacific Journal of Mathematics, vol. 10, pp.
–334, 1960.
C. Ionescu, S. Rezapour, and M. E. Samei, “Fixed points of some new contractions on intuitionistic
fuzzy metric spaces,” Fixed Point Theory and Applications, vol. 2013, article 168, 2013.
N. Hussain, S. Khaleghizadeh, P. Salimi, and Afrah A. N. Abdou, “A New Approach to Fixed Point
Results in Triangular Intuitionistic Fuzzy Metric Spaces”, Abstract and Applied Analysis, Volume
, Article ID 690139, 16 pages.
Marta Demma and Pasquale Vetro, Picard Sequence and Fixed point Results on b-metric spaces,
Journal of Function Spaces, vol.2015, Article ID 189861 6 pages.
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inf. Univ. Ostravensis, 1 (1993),
-11.
S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis.
Univ. Modena, 46 (1998), 263-276.
M. A. Alghamdi, N. Hussain, P. Salimi, Fixed point and coupled fixed point theorems on b-metriclike
spaces, J. Inequal. Appl., 2013 (2013), 25 pages.
N. Hussain, V. Parvaneh, J. R. Roshan, Z. Kadelburg, Fixed points of cyclic weakly ( )-
contractive mappings in ordered b-metric spaces with applications, Fixed Point Theory Appl., 2013
(2013), 18pages.
R. Jain, R. D. Daheriya and M. Ughade, Fixed Point, Coincidence Point and Common Fixed
Point Theorems under Various Expansive Conditions in Parametric Metric Spaces and Parametric b-
Metric Spaces, Gazi University Journal of Science, Accepted, 2015.