Mappings In Metric Spaces Research Articles

Fixed points of mappings of metric spaces

A survey of the theory of fixed points of mappings of metric spaces, containing some unpublished results of the author, is presented.

A Common Fixed Point Theorem for a Sequence of Multivalued Mappings

Recently, fixed point theorems for multivalued contraction mappings in metric spaces were obtained by many authors ( [5] , [2] , [7] , [1] , [4] , [6] , etc) . On the other hand, Dube [3] proved a theorem on common fixed points of two multivalued mappings. In this paper, we shall give a common fixed point theorem for a sequence of multivalued mappings satisfying some conditions in complete metric spaces. In our theorem, we shall obtain an extension of the result of Itoh [4] to the case of a sequence of multivalued mappings.

Fixed point theorems for nonexpansive mappings in a locally convex space

Several fixed point theorems for nonexpansive self mappings in metric spaces and in uniform spaces are known. In this context the concept of orbital diameters in a metric space was introduced by Belluce and Kirk. The concept of normal structure was utilized earlier by Brodskiĭ and Mil'man. In the present paper, both these concepts have been extended to obtain definitions of β-orbital diameter and β-normal structure in a uniform space having β as base for the uniformity. The closed symmetric neighbourhoods of zero in a locally convex space determine a base β of a compatible uniformity. For 3-nonexpansive self mappings of a locally convex space, fixed point theorems have been obtained using the concepts of β-orbital diameter and β-normal structure. These theorems generalise certain theorems of Belluce and Kirk.

On the k-ness for the products of closed images of metric spaces

The product of images, under closed maps of metric spaces need not be a k-space. In view of these maps, we shall give some necessary conditions for products to be k-spaces.

Multi-valued contraction mappings in metric spaces

Some fixed point theorems for multi-valued contraction mappings in metric spaces, related to a fixed point theorem due to T. Zamfirescu [6], [5], are presented.

Multi-valued contraction mappings in metric spaces

Multi-valued contraction mappings in metric spaces

On a Theorem of Mitchell

In this note we apply a theorem of T. Mitchell on fixed points of contraction maps to a particular set of contraction maps of metric spaces. Also, part of Mitchell's theorem is extended to permit application, under suitable conditions, when the space involved is not compact.We employ the following terminology due to Mitchell [1]. Let S be a semigroup; m(S) the space of all bounded real functions on S with sup norm; and X a subset of m(S). For all s ∊ S, the left translation ls {right translation rs} of m(s) by s is given by (lsf)(s') = f(ss') {(rsf)(s')=f(s's)} where f ∊ m(S) and s' ∊ S.

Common Fixed Point for Weakly Compatible Maps in Metric Space

A common fixed point theorem involving two pairs of weakly compatible mappings is proved under a Lipschitz type contractive condition, which is independent of the known contractive definitions. Keywords: fixed point; complete metric space; weakly compatible maps. DOI: 10.3126/kuset.v3i2.2893 Kathmandu University Journal of Science, Engineering and Technology Vol.3, No.2, August 2007, pp 21-26

A fixed point theorem for nonexpansive mappings in metric space

A fixed point theorem for nonexpansive mappings in metric space

On the Product of Real Valued Uniformly Continuous Functions in Metric Spaces

On the Product of Real Valued Uniformly Continuous Functions in Metric Spaces

On the Product of Real Valued Uniformly Continuous Functions in Metric Spaces

On the Product of Real Valued Uniformly Continuous Functions in Metric Spaces

On the Product of Real Valued Uniformly Continuous Functions in Metric Spaces

On the Product of Real Valued Uniformly Continuous Functions in Metric Spaces

On a property of mappings of metric spaces

On a property of mappings of metric spaces

Covering Theorems with respect to the Set Function in Metric Space

Covering Theorems with respect to the Set Function in Metric Space