The regular open continuous images of complete metric spaces

On weak-open compact images of metric spaces

To find internal characterizations of certain images of metric spaces is one of central problems in general topology. Arhangel’skiı̆ [1] showed that a space is an open compact image of a metric space if and only if it has a development consisting of point-finite open covers, and some characterizations for certain quotient compact images of metric spaces are obtained in [3, 5, 8]. Recently, Xia [...

Complete Metric Spaces

Complete Generalized Metric Spaces

The well-known Banach’s fixed point theorem asserts that ifD X, f is contractive and X, d is complete, then f has a unique fixed point inX. It is well known that the Banach contraction principle 1 is a very useful and classical tool in nonlinear analysis. In 1969, Boyd and Wong 2 introduced the notion ofΦ-contraction. A mapping f : X → X on a metric space is called Φ-contraction if there exists...

On Generalized Complete Metric Spaces

Generalized multivalued $F$-weak contractions on complete metric spaces

In this paper,  we introduce the notion of  generalized multivalued  $F$- weak contraction and we prove some fixed point theorems related to introduced  contraction for multivalued mapping in complete metric spaces.  Our results extend and improve the results announced by many others with less hypothesis. Also, we give some illustrative examples.