Metric dimension of complete metric spaces

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

Cohomological Dimension Theory of Compact Metric Spaces

0. Introduction 1 1. General properties of the cohomological dimension 2 2. Bockstein theory 6 3. Cohomological dimension of Cartesian product 10 4. Dimension type algebra 15 5. Realization theorem 19 6. Test spaces 24 7. Infinite-dimensional compacta of finite cohomological dimension 28 8. Resolution theorems 33 9. Resolutions preserving cohomological dimensions 41 10. Imbedding and approximat...

Generalized multivalued $F$-contractions on complete metric spaces

In the present paper‎, ‎we introduce the concept of generalized multivalued $F$ -‎contraction mappings and give a fixed point result‎, ‎which is a proper‎ ‎generalization of some multivalued fixed point theorems including Nadler's‎.