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- B. Nanjaras, Bancha Panyanak, M. A. Khamsi
- 2010

One of the fundamental and celebrated results in the theory of nonexpansive mappings is Browder’s demiclosed principle 1 which states that if X is a uniformly convex Banach space, then C is a nonempty closed convex subset of X, and if T : C → X is a nonexpansive mapping, then I−T is demiclosed at each y ∈ X, that is, for any sequence {xn} inC conditions xn… (More)

- M. A. Khamsi
- 2004

The author would like to thank Colegio El Pinar for their hospitality during the preparation of this survey.

- M. A. Khamsi
- 2004

In hyperconvex metric spaces, we introduce Knaster-KuratowskiMazurkiewicz mappings (in short KKM-maps). Then we prove an analogue to Ky Fan fixed point theorem in hyperconvex metric spaces.

- G. Jungck, Stojan Radenovic, S. Radojevic, Vladimir Rakocevic, M. A. Khamsi
- 2009

Recommended by Mohamed Khamsi We prove several fixed point theorems on cone metric spaces in which the cone does not need to be normal.

- M. A. Khamsi
- 2010

We discuss the newly introduced concept of cone metric spaces. We also discuss the fixed point existence results of contractive mappings defined on such metric spaces. In particular, we show that most of the new results are merely copies of the classical ones.

We discuss the existence of fixed points of asymptotic pointwise mappings in metric spaces. This is the nonlinear version of some known results proved in Banach spaces. We also discuss the case of multivalued mappings. MSC: Primary 47H09; Secondary 47H10.

The existence of approximate fixed points and approximate endpoints of the multivalued almost I-contractions is established. We also develop quantitative estimates of the sets of approximate fixed points and approximate endpoints for multivalued almost I-contractions. The proved results unify and improve recent results of Amini-Harandi 2010 , M. Berinde and… (More)

In this paper, we show that nonempty closed convex subsets of a metric tree enjoy many properties shared by convex subsets of Hilbert spaces and admissible subsets of hyperconvex spaces. Furthermore, we prove that a set valued mapping T ∗ of a metric tree M with convex values has a selection T : M → M for which d(T (x), T (y)) ≤ dH(T ∗(x), T ∗(y)) for each… (More)

Let X, d be a metric space and x, y ∈ X with l d x, y . A geodesic path from x to y is an isometry c : 0, l → X such that c 0 x and c l y. The image of a geodesic path is called a geodesic segment. A metric spaceX is a (uniquely) geodesic space if every two points ofX are joined by only one geodesic segment. A geodesic triangle x1, x2, x3 in a geodesic… (More)