In this work, we prove that modular spaces Vρ(λ; p) defined in  have the k-nearly uniform convexity(k−NUC property) when they are endowed with the Luxemburg norm. We also prove that these spaces have the uniform Opial property with the Luxemburg norm. The above investigated geometric properties will enable us to obtain some fixed point results in modular spaces.
ŞİMŞEK, Necip; SAVAŞ, Ekrem; and KARAKAYA, Vatan
"On Geometrical Properties of Some Banach Spaces,"
Applied Mathematics & Information Sciences: Vol. 07:
1, Article 37.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol07/iss1/37