B. E. Rhoades

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We establish two fixed-point theorems for mappings satisfying a general contrac-tive inequality of integral type. These results substantially extend the theorem of Branciari (2002). In a recent paper [1], Branciari established the following theorem. Theorem 1. Let (X, d) be a complete metric space, c ∈ [0, 1), f : X → X a mapping such that, for each x, y ∈(More)
Let £ be a closed, bounded, convex subset of a Banach space X, /: E —»E. Consider the iteration scheme defined by x"« = xQ e E, x , = ñx ), x = 2" na ,x., nal, where A is a regular weighted mean n + l ' n n * = 0 nk k o er matrix. For particular spaces X and functions /we show that this iterative scheme converges to a fixed point of /. Let X be a normed(More)
Huang and Zhang [L.-G. Haung, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468–1476] proved some fixed point theorems in cone metric spaces. In this work we prove some fixed point theorems in cone metric spaces, including results which generalize those from Haung and Zhang’s work. Given the(More)
Recommended by Massimo Furi We obtain several fixed point theorems for hybrid pairs of single-valued and multivalued occasionally weakly compatible maps defined on a symmetric space satisfying a contrac-tive condition of integral type. The results of this paper essentially contain every theorem on hybrid and multivalued self-maps of a metric space as a(More)
In this paper we prove two fixed point theorems for the generalized metric spaces introduced by Dhage. In a recent paper, Dhage [1] defined a generalized metric space as follows: Let D:X x X x X R with the following properties: (i) D(x, y, z) >_ 0 for each x, y, z X, with equality if and only if x y z, (ii) D(x, y, z) D(y, x, z) D(x, z, y) (symmetry) (iii)(More)
The existence of coincidence points and common fixed points for four mappings satisfying generalized contractive conditions without exploiting the notion of continuity of any map involved therein, in a cone metric space is proved. These results extend, unify and generalize several well known comparable results in the existing literature. 2010 Elsevier Inc.(More)
This paper provides a survey of iteration procedures that have been used to obtain fixed points for maps satisfying a variety of contractive conditions. The author does not claim to provide complete coverage of the literature, and admits to certain biases in the theorems that are cited herein. In spite of these shortcomings, however, this paper should be a(More)
New fixed point results for a pair of non-self mappings defined on a closed subset of a metrically convex conemetric space which is not necessarily normal are obtained. By adapting Assad-Kirk’s method the existence of a unique common fixed point for a pair of non-self mappings is proved, using only the assumption that the cone interior is nonempty. Examples(More)