Some Fixed Point Results in Partial Metric Spaces Under Contractive Type Mappings


Affiliations

  • Govt. K. P. G. College Jagdalpur, Department of Mathematics, Jagdalpur, Chhattisgarh, 494001, India

Abstract

In this paper, we establish some fixed point theorems and a coincidence point theorem for contractive type mappings in the framework of complete partial metric spaces and give some examples in support of our results. The results presented in this paper extend and generalize several results from the existing literature.

Keywords

Fixed point, contractive type mapping, partial metric space

Full Text:

References

T. Abdeljawad, E. Karapinar and K. Tas, Existence and uniqueness of common fixed point partial metric spaces, Appl. Math. Lett. in press (doi:10.1016/j.aml.2011.05.014).

H. Aydi, M. Abbas and C. Vetro, Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric spaces, Topology and Its Appl., 159. (14) (2012), 3234 - 3242.

S. Banach, Surles operation dans les ensembles abstraits et leur application aux equation integrals, Fund. Math., 3. (1922), 133 - 181.

I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal. Gos. Ped. Inst. Unianowsk, 30. (1989), 26 - 37.

M. Bukatin, R. Kopperman, S. G. Matthews and H. Pajoohesh, Partial metrispaces, The Mathematical Assoc. of America, 116. (2009), 708 - 718.

S. K. Chatterjae, Fixed point theorems compactes, Rend. Acad. Bulgare Sci., 25. (1972), 727 - 730.

L. -G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332. (2) (2007), 1468 - 1476.

N. Hussain and MH. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl., 62. (2011), 1677 - 1684.

R. Kannan, Some results on fixed point theorems, Bull. Calcutta Math. Soc., 60. (1969), 71 - 78.

O. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11. (1975), 326 - 334.

H. P. A. K¨unzi, Nonsymmetric distances and their associated topologies about the origins of basic ideas in the area of asymptotic topology, Handbook of the History Gen. Topology (eds. C.E. Aull and R. Lowen), Kluwer Acad. Publ., 3. (2001), 853 - 868.

S. G. Matthews, Partial metric topology, Research report 2012, Deptt. Ccmputer Science, University of Warwick, 1992.

S. G. Matthews, Partial metric topology, Proceedings of the 8th summer conference on topology and its applications, Annals of the New York Academy of Sciences, 728. (1994), 183 - 197.

H. K. Nashine, Z. Kadelburg, S. Radenovic and J. K. Kim, Fixed point theorems under Hardy-Rogers contractive conditions on 0-complete ordered partial metric spaces, Fixed Point Theory Appl., 2012. (2012), 1 - 15.

O. Vetro, On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topology, 6. (12) (2005), 229 - 240.


Refbacks

  • There are currently no refbacks.