Abstract
We prove that modular spaces L ρ have the uniform Kadec–Klee property w.r.t. the convergence ρ-a.e. when they are endowed with the Luxemburg norm. We also prove that these spaces have the uniform Opial condition w.r.t. the convergence ρ-a.e. for both the Luxemburg norm and the Amemiya norm. Some assumptions over the modular ρ need to be assumed. The above geometric properties will enable us to obtain some fixed point results in modular spaces for different kind of mappings.
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