The fixed point theory in modular function spaces originated in the 1990 seminal paper by Khamsi, Kozlowski and Reich [3].
From this perspective, the fixed point theory in modular metric spaces should be considered as complementary to the fixed point theory in modular function spaces and in metric spaces.
The importance of applications of nonexpansive mappings in modular function spaces lies in the richness of structure of modular function spaces, that is, besides being Banach spaces (or F-spaces in a more general setting --are equipped with modular equivalentsetting --aremetric notionsetting --arerequippeded with almodularequivalentsnvergence and cofvergenormin submeasure.
The importance of applications of nonexpansive mappings in modular function spaces lies in the richness of structure of modular function spaces that besides being Banach spaces (or F-spaces in a more general settings) are equipped with modular equivalents of norm or metric notions, and also are equipped with almost everywhere convergence and convergence in submeasure.
The importance for applications of nonexpansive mappings in modular function spaces consists in the richness of structure of modular function spaces, that-besides being Banach spaces (or F-spaces in a more general settings -are equipped with modular equivalentsettings -aremequippedtions, and also are equipped with almodularequivalentsnvergence and cofvergenormin submeasure.
Earlier studies of fixed point theory in modular function spaces can be found in [2 4], see also [5].
The importance for applications of mappings defined within modular function spaces consists in the richness of the structure of modular function spaces, which, besides being Banach spaces, are equipped with modular equivalents of norm or metric notions and also are equipped with almost everywhere convergence and convergence in sub-measure.
Overall the hemilineages appear to have a modular function with cells in a given group being associated with particular behavioral responses.
These data confirm a modular function of CR1 in SWI/SNF recruitment and show the feasibility of proteomic expression screening approaches with transactivation modules that contain or lack post-translational modifications to uncover differential protein interactions.
In the context of modular function spaces, Khamsi discussed in [12] the existence of nonlinear semigroups in Musielak-Orlicz spaces and considered some applications to differential equations.
