Mizoguchi-Takahashi’s type common fixed point theorems without T-weakly commuting condition and invariant approximations (original) (raw)
Abstract
Recently Kamran extended the result of Mizoguchi and Takahashi for closed multivalued mappings and proved a fixed point theorem. In this paper we further extend the result concluded by Kamran and prove a common fixed point theorem by using the concept of lower semi-continuity. 2000 MATHEMATICS SUBJECT CLASSIFICATION: 54H25 ª 2013 Production and hosting by Elsevier B.V. on behalf of Egyptian Mathematical Society.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.
References (10)
- T. Kamran, Coincidence and fixed points for hybrid strict contractions, J. Math. Anal. Appl. 299 (2004) 235-241.
- T.L. Hicks, B.E. Rhoades, A banach type fixed point theorem, Math. Japon. 24 (1979) 327-330.
- S.B. Nadler Jr., Multivalued contraction mappings, Pacific J. Math. 30 (1969) 475-488.
- S. Reich, Fixed points of contractive functions, Boll. Unione Mat. Ital. 4 (5) (1972) 26-42.
- N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric space, J. Math. Anal. Appl. 141 (1989) 177-188.
- P.Z. Daffer, H. Kaneko, Fixed points of generalized contractive multi-valued mappings, J. Math. Anal. Appl. 192 (1995) 655- 666.
- T.H. Chang, Common fixed point theorems for multi-valued mappings, Math. Japon. 41 (1995) 311-320.
- A.A. Eldred, J. Anuradha, P. Veeramani, On equivalence of generalized multi-valued contractions and Nadler's fixed point theorem, J. Math. Anal. Appl. (2007), http://dx.doi.org/10.1016/ j.jmaa.2007.01.087.
- T. Suzuki, Mizoguchi-Takahashi's fixed point theorem is a real generalization of Nadler's, J. Math. Anal. Appl. (2007), http:// dx.doi.org/10.1016/j.jmaa.2007.08.022.
- T. Kamran, Mizoguchi-Takahashi's type fixed point theorem, Comput. Math. Appl. 57 (2009) 507-511.