Let f be
bounded function of soft sets attaining the bound parameterwise in an interior point of [mathematical expression not reproducible] and differentiable on [mathematical expression not reproducible].
We point out that in [6] the authors considered M(x, u) as a
bounded function and
N'Gucrekata, Spectral Theory for
Bounded Functions and Applications to Evolution Equations, Nova Science Publishers, New York, NY, USA, 2017.
If [mathematical expression not reproducible] is a
bounded function on [mathematical expression not reproducible] and [[absolute value of u].sup.2](z) [[absolute value of v].sup.2] (z) are both bounded on [C.sup.n].
for some positive number [[lambda].sub.0], where p(t) is a nonnegative
bounded function. Suppose further that
Moreover, assume that there exists a
bounded function [[gamma].sub.2] : [0, [infinity]) [right arrow] [0, [infinity]) with li[m.sub.t[right arrow]0]+ [[gamma].sub.2](t) = 0 such that
where r is a
bounded function, ([[epsilon].sub.t]) is a square integrable process, and et and ([X.sub.t]) are independent.
Suppose that, for each n [greater than or equal to] 0, [u.sub.n] (r) is a
bounded function for a [less than or equal to] r [less than or equal to] b.
In the recent paper [10], Theorem 3.2 (iv), applying this idea to the classical Whittaker's cardinal series, we have obtained a Jackson-type estimate in terms of [[omega].sub.1][(f; 1/W).sub.R], in approximation of a continuous, positive and
bounded function f on R, by the nonlinear max-product Whittaker sampling operator given by
with a
bounded function a [member of] [L.sup.2] (0, [infinity]) satisfying the inequality [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Let q > 1 and f : [0,1] [right arrow] C be a
bounded function, such that f [member of] C[0, a], 0 < a [less than or equal to] 1.
If f : {1,2, ..., N} x R [right arrow] R is a continuous and
bounded function, then BVP (2.2) has a solution.