Sentence examples for the general operator from inspiring English sources
So, we make a general characterization for the general operator (T_{n}[M]) and we avoid the necessity of calculating the Green's function and to study its sign dependence on the real parameter M.
In the context, we shall use either ({mathcal {F}}) or F to denote the general operator in (1.1), and either ({mathcal {G}}) or G to denote the boundary operator in (1.2).
For the general operator M Ω P, when P N i ( t ) = t ( i = 1, 2 ) and φ, ψ ∈ F, Al-Salman [3] showed that M Ω P is bounded on L p ( R m × R n ) for 1 < p < ∞ provided that Ω ∈ L log + L ( S m − 1 × S n − 1 ).
However, for various applications it is also important to consider the mapping properties of the more general operator (H_{k}(f)(x):=int_{0}^{x}k x,t f(t),dt), where (k x,t)) is a kernel (a non-negative and measurable function on ({(x,t):0leq x
The main contribution of this paper lies in generalizing this operator in three different ways: to also include matrix-valued potential functions as in Eq. (1.5), to the more general operator in Eq. (1.4), and lastly to settings where the operator acts on functions defined on subsets of the real line.
By imposing supplimentary conditions for these functions we proved some univalent conditions for the considered general operator.
This paper describes the advancement of performance of simple SA applied upon the problem of graph coloring using a specially designed operator called random change operator instead of the general change operator.
The importance of the Dziok-Srivastava operator from the general convolution operator rests on the relation (1.11).
(3.7) Here the (L=D_{t}^{alpha}), R is the linear differential operator, N represents the general nonlinear operator and (h x,t)) is the nonhomogeneous source term.
Note that in [6] the above results were generalized to the case of considerably more general operator ideals.
(2) If is a Hilbert space, then the general -monotone operator reduces to the -monotone operator in Verma [7].
