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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access September 2, 2014

Unique Common Fixed Point Theorems for Pairs of Hybrid Maps under a New Condition in Partial Metric Spaces

  • K. P. R. Rao EMAIL logo and K. R. K. Rao
From the journal Demonstratio Mathematica

Abstract

In this paper, we introduce a new condition namely, ‘condition (W.C.C)’ and obtain two unique common fixed point theorems for pairs of hybrid mappings on a partial Hausdorff metric space without using any continuity and commutativity of the mappings.

References

[1] B. Damjanovic, B. Samet, C. Vetro, Common fixed point theorems for multi-valued maps, Acta Math. Sci. (English Ed.) 32 (2012), 818-824.10.1016/S0252-9602(12)60063-0Search in Google Scholar

[2] B. D. Rouhani, S. Moradi, Common fixed point of multivalued generalized _-weak contractive mappings, Fixed Point Theory Appl. vol. 2010, Artical ID 708984, 13 pages.10.1155/2010/708984Search in Google Scholar

[3] C. Di Bari, P. Vetro, Fixed points for weak _-contractions on partial metric spaces, Int. J. Contemp. Math. Sci. 1(1) (2011), 5-13.10.1186/1687-1812-2012-140Search in Google Scholar

[4] C. Di Bari, Z. Kadelburg, H. K. Nashine, S. Radenovic, Common fixed points of g-quasicontractions and related mappings in 0-complete partial metric spaces, Fixed Point Theory Appl. vol. 2012, 2012:113, 13 pages.10.1186/1687-1812-2012-113Search in Google Scholar

[5] C. Di Bari, M. Milojevic, S. Radenovic, P. Vetro, Common fixed points for selfmappings on partial metric spaces, Fixed Point Theory Appl. vol. 2012, 2012:140, 10 pages.10.1186/1687-1812-2012-140Search in Google Scholar

[6] D. Paesano, P. Vetro, Suzki’s type characterization of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl. 159(3) (2012), 911-920.10.1016/j.topol.2011.12.008Search in Google Scholar

[7] F. Vetro, S. Radenovic, Nonlinear -quasi-contractions of Ciric-type in partial metric spaces, Appl. Math. Comput. 219 (2012), 1594-1600.Search in Google Scholar

[8] H. Covitz, S. B. Nadler Jr., Multi-valued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5-11.10.1007/BF02771543Search in Google Scholar

[9] H. Aydi, M. Abbas, C. Vetro, Partial Hausdrouff metric and Nadler’s fixed point theorem on partial metric space, Topology Appl. 159(14) (2012), 3234-3242.10.1016/j.topol.2012.06.012Search in Google Scholar

[10] I. Altun, H. Simsek, Some fixed point theorems on dualistic partial metric spaces, J. Adv. Math. Stud. 1 (2008), 1-8.Search in Google Scholar

[11] I. Altun, F. Sola , H. Simsek, Generalized contractions on partial metric spaces, Topology Appl. 157 (2010), 2778-2785.10.1016/j.topol.2010.08.017Search in Google Scholar

[12] K. P. R. Rao, G. N. V. Kishore, A unique common fixed point theorem for four maps under p_q contractive condition in partial metric spaces, Bull. Math. Anal. Appl. 3(3) (2011), 56-63.10.20454/jast.2012.193Search in Google Scholar

[13] K. P. R. Rao, G. N. V. Kishore, K. A. S. N. V. Prasad, A unique common fixed point theorem for two maps under p_q contractive condition in partial metric spaces, Math. Sci. (Springer open Journal), 6:9, 2012, 4 pages.10.1186/2251-7456-6-9Search in Google Scholar

[14] Lj. Ciric, Fixed points for generalized multi-valued contractions, Mat. Vesnik 9 (1972), 265-272.Search in Google Scholar

[15] Lj. Ciric, Multi-valued nonlinear contraction mappings, Nonlinear Anal. 71 (2009), 2716-2723.10.1016/j.na.2009.01.116Search in Google Scholar

[16] Lj. Ciric, B. Samet, H. Aydi, C. Vetro, Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput. 218 (2011), 2398-2406.Search in Google Scholar

[17] M. Kikkawa, T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal. 69 (2008), 2942-2949.10.1016/j.na.2007.08.064Search in Google Scholar

[18] N. Mizoguchi, W. Takahashi, Fixed point theorems for multi-valued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989), 177-188.10.1016/0022-247X(89)90214-XSearch in Google Scholar

[19] P. Z. Daffer, H. Kaneko, Fixed points of generalized contractive multi-valued mappings, J. Math. Anal. Appl. 192(2) (1995), 655-666.10.1006/jmaa.1995.1194Search in Google Scholar

[20] S. B. Nadler, Mutivalued contraction mappings, Pacific. J. Math. 30 (1969), 475-488.10.2140/pjm.1969.30.475Search in Google Scholar

[21] S. G. Matthews, Partial metric topology, Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci. vol. 728, 1994, 183-197.10.1111/j.1749-6632.1994.tb44144.xSearch in Google Scholar

[22] S. Romaguera, A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory Appl. vol. 2010, Article ID 493298, 6 pages. 10.1155/2010/493298Search in Google Scholar

Received: 2013-3-11
Revised: 2013-10-28
Published Online: 2014-9-2
Published in Print: 2014-7-1

© by K. P. R. Rao

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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