A common fixed point theorem for a sequence of maps in a generalized Menger space
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The object of this paper is to establish a unique common fixed point theorem through weak compatibility for a sequence of self-maps satisfying a generalized contractive condition in a generalized Menger space. It improves and generalizes the result of Milovanovic-Arandelovic [2], Vasuki [10] and Sehgal and Bharucha-Reid [8]. All the results presented in this paper are new.
Abstract
The object of this paper is to establish a unique common fixed point theorem through weak compatibility for a sequence of self-maps satisfying a generalized contractive condition in a generalized Menger space. It improves and generalizes the result of Milovanovic-Arandelovic [2], Vasuki [10] and Sehgal and Bharucha-Reid [8]. All the results presented in this paper are new.
참고문헌 (10)
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- Shishir Jain, "Semi-Compatibility and common fixed poin theorems in abstract spaces", Ph. D., pp.2005
- Shobha Jain, "A study of common fixed poin theorems through weak compatibility in abstract spaces", Ph. D., pp.2005
- G. Jungck, "Fixed points for set valued functions without continuity", Indian J. of Pure and Applied Mathematics, 29, pp.227~238 (1998)
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- B. Schweizer, "Statistical metric spaces", Pacific J. Math, 10, pp.313~334 (1960)
- V. M. Sehgal, "Fixed points of contraction mappings in PMspaces", Math. Systems Theory, 6, pp.97~102 (1972)
- B. Singh, "A fixed point theorem in Menger space through weak compatibility", Journal of Mathematical Analysis and Application, 301, pp.439~448 (2005)
- R. Vasuki, "A fixed point theorem for sequence of maps satisfying a new contraction type condition in Menger space", Math. Japonica, 35(6), pp.535~539 (1989)