Improving Many Metric Fixed Point Theorems

Authors

Sehie Park

Keywords:

Quasi-metric space, fixed point, RHR contraction principle, orbitally complete, orbitally continuous

Abstract

We found that many metric fixed point theorems hold for orbitally complete quasi-metric spaces. In order to show this, we obtain several basic principles extending the Banach contraction principle and new fixed point theorems for the Rus-Hicks-Rhoades maps with a large number of their consequences. Moreover, we improve theorems on mappings with contractive conditions with some auxiliary functions and on mappings with asymptotically regularity. Consequently, a large number of known metric fixed point theorems are extended with almost trivial short proofs.

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