We prove the existence of fixed points of monotone quasi-contraction mappings in metric and modular metric spaces. This is the extension of Ran and Reurings fixed point theorem for monotone contraction mappings in partially ordered metric spaces to the case of quasicontraction mappings introduced by Ćirić. The proofs are based on Lemmas ?? and ??, which contain two crucial inequalities essentia...

As a generalization to Banach contraction principle, Ćirić introduced the concept of quasi-contraction mappings. In this paper, we investigate these kind of mappings in modular function spaces without the ∆2-condition. In particular, we prove the existence of fixed points and discuss their uniqueness. 2000 Subject Classification: Primary 46E30; Secondary 47H09, 47H10.

Using a mixture of analytic and numerical techniques we show that the mode-locked regions of quasi-periodically forced Arnold circle maps form complicated sets in parameter space. These sets are characterized by ‘pinched-off’ regions, where the width of the mode-locked region becomes very small. By considering general quasi-periodically forced circle maps we show that this pinching occurs in a ...

The contraction processes of metal-free molecular clouds of starlike mass (or cloud cores) are investigated. We calculate radiative transfer of the H2 lines and examine quasi-static contraction with radiative cooling. Comparing two time-scales, the free-fall time tff and the time-scale of quasi-static contraction tqsc (∼ tcool, the cooling time) of these cores, we find that the ratio of the two...