Nonlinear quasicontractions in complete metric spaces

Generalized Quasicontractions in Orbitally Complete Abstract Metric Spaces

Some fixed point results for generalized quasicontractions in abstract metric spaces obtained recently are extended to the case of a pair of mappings. Also, it is shown that in some cases regularity and/or normality condition for the underlying cone can be dropped. Examples are given to illustrate the results.

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.