### FIXED POINTS OF GENERALIZED (ALPHA, PSI,PHI)-CONTRACTIVE MAPS AND PROPERTY(P) IN S-METRIC SPACES

**DOI Number**

**First page**

**Last page**

#### Abstract

In this paper, we introduce generalized (alpha, psi,phi)-contractive maps and prove

the existence and uniqueness of xed points in complete S-metric spaces. We also

prove that these maps satisfy property (P). We discuss the importance of study of the existence of xed points in S-metric space rather than in the setting of metric space.The results presented in this paper extends several well known comparable results in metric and G-metric spaces. We provide example in support of our result.

#### Keywords

#### Full Text:

PDF#### References

J. M. Afra, Fixed Point Type Theorem In S-Metric Spaces (II), Theory of Approximation and Applications, 10(1), (2014), 57-68.

J. M. Afra, Double Contraction in S-Metric Spaces, International Journal of Mathematical Analysis, 9(3), (2015), 117 - 125.

G. V. R. Babu, D. R. Babu, K. N. Rao and B. V. S. Kumar, Fixed Points

of (psi,phi)-Almost Weakly Contractive Maps In G-Metric Spaces, Applied Mathematics E-Notes, 14 (2014), 69-85, (2014).

M. Bousselsal and S. Hamidou Jah, Property(P) and some xed point results on a new phi -weakly contractive mapping, Adv. Fixed Point Theory, 4(2), (2014), 169-183.

D. W. Boyd and J. S. W. Wong, On nonlinear contractions, Proceedings of the American Mathematical Society, 20(2), (1969), 458-464.

R. Chugh, T. Kadian, A. Rani, B. E. Rhoades, Property P in G-metric spaces, Fixed Point Theory Appl., (2010), Article ID 401684, 12 pages, (2010).

B. C. Dhage, Generalized metric spaces mappings with fixed point, Bull. Calcutta Math. Soc., 84 (1992), 329-336, (1992).

N. V. Dung, N. T. Hieu, S. Radojevic, Fixed Point Theorems for g-Monotone Maps on Partially Ordered S-Metric Spaces, Published by Faculty of Sciences and Mathematics, University of Nis, Serbia, Filomat 28:9 2014, 1885-1898 DOI 10.2298/FIL1409885D,

(2014).

G. S. Jeong and B. E. Rhoades, Maps for which F(T) = F(Tn), Fixed Point Theory and Applications, 6, 71-105, Nova Science Publishers, New York, NY, USA, (2007).

G. S. Jeong and B. E. Rhoades, More maps for which F(T) = F(Tn), Demonstratio Mathematica, 40(3), 671-680, (2007).

M. S. Khan, M. Swaleh and S. Sessa, Fixed point theorems by altering distance between points, Bull. Aust. Math. Soc., 30(1), (1984), 1-9.

Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7, (2006), 289-297.

Z. Mustafa, H. Obiedat, F. Awawdeh, Some common xed point theorems for mapping on complete G-metric spaces, Fixed Point Theory Appl., 2008, Article ID 189870, 12

pages, (2008).

S. Sedghi, K.P.R. Rao, N. Shobe, Common xed point theorems for six weakly compatible mappings in D*-metric spaces, Internat. J. Math. Math. Sci., 6 (2007), 225-237.

S. Sedghi, N. Shobe, H. Zhou, A common xed point theorem in D*-metric spaces, Fixed Point Theory Appl., 2007, Article ID 27906, 13 pages (2007).

S. Sedghi, N. Shobe, A. Aliouche, A generalization of xed point theorem in S-metric spaces, Math. Vesnik, 64 (2012), 258 - 266.

S. Sedghi and N. V. Dung, Fixed point theorems on S-metric spaces, Math. Vesnik 66 (2014), 113 -124.

W. Shatanawi, Fixed point theory for contractive mappings satisfying phi-maps in G-metric spaces, Fixed Point Theory Appl., (2010), Article ID 181650, 9 pages, (2010).

DOI: https://doi.org/10.22190/FUMI200730026B

### Refbacks

- There are currently no refbacks.

ISSN 0352-9665 (Print)