Points of monotonicity in Orlicz–Lorentz function spaces

Abstract

In Orlicz–Lorentz function space ⋀ M , ω [ 0 , γ ) , points of upper monotonicity, lower monotonicity, upper local uniform monotonicity ( γ < ∞ ) and lower local uniform monotonicity ( γ < ∞ ) are characterized. As the corollary, we can easily obtain the criteria for strict monotonicity, upper local uniform monotonicity ( γ < ∞ ) and lower local uniform monotonicity ( γ < ∞ ) of ⋀ M , ω [ 0 , γ ) .