فهرست نشریات علمی دسترسی آزاد ایران

This paper provides a comprehensive study of geometric properties of variable-exponent Lebesgue-Bochner spaces $L^{p(\cdot)}(E‎, ‎X)$‎. ‎We establish that $L^{p(\cdot)}(E‎, ‎X)$ has the Radon-Nikodym property (RNP) if and only if $X$ does‎, ‎under the condition $p_m > 1$‎. ‎We investigate dentability of specific subsets‎, ‎showing that while the unit ball inherits dentability from $X$‎, ‎the set of simple functions may remain nondentable even when the space possesses RNP‎. ‎The perseverance of uniform convexity and smoothness are shown when both $X$ and $L^{p(\cdot)}(E)$ have these properties‎. ‎We introduce quantitative dentability moduli and relate the dentability modulus of $L^{p(\cdot)}(E,X)$ to that of $X$‎, ‎showing the relevance to the measure of $E$‎, ‎and the oscillation of $p(\cdot)$‎. ‎The paper reveals how variable exponents create hybrid geometries mixing $L^1$ and $L^p$ behaviors‎, ‎with implications for PDE theory‎, ‎optimization‎, ‎and geometric analysis‎.