FIXED POINT THEOREMS IN CONVEX PARTIAL METRIC SPACES

Abstract

Partial metric spaces were introduced by S. G. Matthews [1] as apart of the study of denotational semantics of dataflow networks, the authorintroduced and studied the concept of partial metric space, and obtained aBanach type fixed point theorem on complete partial metric spaces. In thispaper, we study some fixed point theorems for self-mappings satisfying certaincontraction principles on a convex complete partial metric space, these theoremgeneralize previously obtained results in convex metric space

Keywords

• Partial metric spaces,convex metric spaces; fixed point theorems

References

1. Matthews, SG: Partial metric topology. In: Proc. 8th Summer Conference on General Topol- ogy and Applications. Ann. New York Acad. Sci., vol. 728, pp. 183-197 (1994).
2. Takahashi, T: A convexity in metric spaces and nonexpansive mapping I. Kodai Math. Sem. Rep. 22, 142-149(1970).
3. Beg, I: An iteration scheme for asymptotically nonexpansive mappings on uniformly convex metric spaces. Nonlinear Analysis Forum. 6:1, 27-34(2001).
4. Beg, I, Abbas, M: Common fixed points and best approximation in convex metric spaces. Soochow Journal of Mathematics. 33:4, 729-738(2007).
5. Beg, I, Abbas, M: Fixed-point theorem for weakly inward multivalued maps on a convex metric space. Demonstratio Mathematica. 39:1, 149-160(2006).
6. Chang, SS, Kim, JK, Jin, DS: Iterative sequences with errors for asymptotically quasi non- expansive mappings in convex metric spaces. Arch. Inequal. Appl. 2, 365-374(2004).
7. Ciric, L: On some discontinuous fixed point theorems in convex metric spaces. Czech. Math. J. 43:188, 319-326(1993).
8. Shimizu, T, Takahashi, W: Fixed point theorems in certain convex metric spaces. Math. Japon. 37, 855-859(1992).

9. Tian, YX: Convergence of an Ishikawa type iterative scheme for asymptotically quasi nonex- pansive mappings. Computers and Maths. with Applications. 49, 1905-1912(2005).
10. Ding, XP: Iteration processes for nonlinear mappings in convex metric spaces. J. Math. Anal. Appl. 132, 114-122(1998).
11. I. Altun, F. Sola, H. Simsek, Generalized contractions on partial metric spaces, Topology Appl. 157 (18) (2010) 2778–2785.
12. S. Romaguera, A kirk type characterization of completeness for partial metric spaces, Fixed Point Theory Appl. (2010) doi:10.1155/2010/493298. 6
13. M. Bukatin, R. Kopperman, S. Matthews, H. Pajoohesh, Partial metric spaces, Amer. Math. Monthly 116 (2009) 708–718. [14] A.F. Rabarison, in: Hans-Peter A. K¨unzi (Ed.), Partial Metrics, African Institute for Math- ematical Sciences, 2007, Supervised.
14. M.A. Bukatin, S.Yu. Shorina, Partial metrics and co-continuous valuations, in: M. Nivat, et al. (Eds.), Foundations of Software Science and Computation Structure, in: Lecture Notes in Computer Science, vol. 1378, Springer, 1998, pp. 125–139.
15. S.G. Matthews, An extensional treatment of lazy data flow deadlock, Theoret. Comput. Sci. 151 (1995) 195–205.
16. S. Romaguera, M. Schellekens, Duality and quasi-normability for complexity spaces, Appl. Gen. Topol. 3 (2002) 91–112. [18] M.P. Schellekens, The correspondence between partial metrics and semivaluations, Theoret. Comput. Sci. 315 (2004) 135–149.
17. M. Moosaei, Fixed Point Theorems in Convex Metric Spaces, Fixed Point Theory and Ap- plications 2012, 2012:164 doi:10.1186/1687-1812-2012-164 Published: 25 September 2012.
18. Current address: Department of Mathematics and Informatic, The Larbi Ben M’hidi Univer- sity, Oum El Bouaghi. 04000, Algeria.
19. E-mail address: taki [e-mail]; [e-mail]
20. Current address: Department of Mathematics , The Larbi Ben M’hidi University, Oum El Bouaghi. 04000, Algeria.
21. E-mail address: [e-mail]