In this paper, we systematically study weighted jump and variational inequalities for rough operators.
As before, we bracket the operator in question between two "rough" operators with the same asymptotics and with sharp remainder estimates.
In this paper, we introduce the generalized central Morrey spaces B ˙ p, φ ( R n ) and get the boundedness of a large class of rough operators on them.
"Bernie meant more to me than I could ever describe to you," Mr. Grey said of Mr. Brillstein, a large, rough-hewn operator who took as much pride in wrangling a deal as his clients took in the creative work that resulted.
Furthermore we also obtain results for rough multilinear operators.
The same properties for the T -upper and the ℐ-lower L-fuzzy rough approximation operators can be obtained.
The condition (1.3) above has been considered by many authors in the context of rough integral operators.
By considering a ring as a universal set, Li et al. [21] studied ( ν, T ) -fuzzy rough approximation operators with respect to a T L -fuzzy ideal of the ring.
In this section, we study the properties of ℐ-lower and T -upper fuzzy rough approximation operators with respect to a T L -fuzzy (full) relational morphism of rings.
The operators Θ ¯ T and Θ ̲ I from F ( Y, L ) to F ( X, L ) are referred to as T -upper and ℐ-lower L-fuzzy rough approximation operators of ( X, Y, Θ ) respectively, and the pair ( Θ ̲ I , Θ ¯ T is called the ( I, T ) -L-fuzzy rofgh set of μ with respect to ( X, Y, Θ ).
