Common fixed point theorems for two pairs of non-self mappings (original) (raw)

Some common fixed point theorems for a family of mappings in metrically convex spaces

Nonlinear Analysis: Theory, Methods & Applications, 2007

In the present paper some common fixed point theorems for a sequence and a pair of nonself-mappings in complete metrically convex metric spaces are proved which generalize such results due to Khan et al. Some fixed point theorems in metrically convex spaces, Georgian Math. J. 7 (3) (2000) 523-530], Assad [N.A. Assad, On a fixed point theorem of Kannan in Banach spaces, Tamkang J. Math. 7 (1976) 91-94], Chatterjea [S.K. Chatterjea, Fixed point theorems, C. R. Acad. Bulgare Sci. 25 (1972) 727-730] and several others. Some related results are also discussed.

Fixed point theorems for a family of hybrid pairs of mappings in metrically convex spaces

Fixed Point Theory and Applications, 2005

The present paper establishes some coincidence and common fixed point theorems for a sequence of hybrid-type nonself-mappings defined on a closed subset of a metrically convex metric space. Our results generalize some earlier results due to Khan et al. (2000), Itoh (1977), Khan (1981), Ahmad and Imdad (1992 and 1998), and several others. Some related results are also discussed.

Common fixed point theorems for nonself-mappings in metrically convex spaces via altering distances

International Journal of Mathematics and Mathematical Sciences, 2005

Some common fixed point theorems for a pair of nonself-mappings in complete metrically convex metric spaces are proved by altering distances between the points, which generalize earlier results due to M. D. Khan and Bharadwaj , M. S. Khan et al. (2000), Bianchini (1972), Chatterjea 1972, and others. Some related results are also discussed besides furnishing an illustrative example. Theorem 1.1. Let (X,d) be a complete metrically convex metric space and K a nonempty closed subset of X. Let T : K → X be a mapping satisfying the inequality d(Tx,T y) ≤ amax d(x,Tx),d(y,T y) + b d(x,T y) + d(y,Tx)

Coincidence and common fixed points of non-self hybrid mappings in metrically convex spaces

Ahmed and Khan obtained some results on common fixed points for a pair of multi-valued and single valued mappings in metrically convex spaces which extends many known results. However the proofs of their results contain some errors. In this paper we rectify these results and prove some common fixed point theorems for a single valued and a pair of multi-valued non self mappings in metrically convex metric spaces. Our results generalize and extends the results of Ciric and

A Common Fixed Point Theorem for a Pair of Nonself Multi-valued Mappings

2012

A common fixed point theorem for a pair of nonself multi-valued mappings in complete metrically convex metric spaces is proved which generalizes some earlier known results due to Khan et al. [9], Bianchini [2], Chatterjea [3], Khan et al. [10] and others. An illustrative example is also discussed.

A fixed point theorem for non-self multi-maps in metric spaces

A fixed point theorem is proved for non-self multi-valued mappings in a met- rically convex complete metric space satisfying a slightly stronger contraction condi- tion than in Rhoades (3) and under a weaker boundary condition than in Itoh (2) and Rhoades (3).

Pair of non-self-mappings and common fixed points

Applied Mathematics and Computation, 2007

We study quasi-contraction type non-self-mappings on Takahashi convex metric spaces and common fixed point theorems for a pair of maps. Results generalizing and unifying fixed point theorems of Imdad and Kumar, Das and Naik, Jungck, Ć irić, Ume, Khan and Pathak, and Ć irić are established.