Sentence examples for involving the function from inspiring English sources

And then we state a Poincare type inequality involving the function, which have been found in [17] and, in a sharp way, in [18].

The so-called First Recursion Theorem (Odifreddi, 1989, II.3.15) provides a basic tool to compute values of functions which are solutions to recursive equations, implicitly defining functions by circular definitions involving the function itself.

For example, it is possible to replace Browder's condition involving the function (psi ) in Theorem 2.2 with a condition introduced in [14] which is a minor variant of a condition due to Geraghty [7].

Simple consequences of the results obtained will include the work of Bharati and Rajagopal [6] involving the function,  , as well as the work of Al-Oboudi and Al-Zkeri [5] on the modified Salagean operator.

Consider the special case, where p = 2, q = 1 in the prolongation formula, so that we are looking at a partial differential equation involving the function u = f x, t).

In this paper, we prove some results on the existence of fixed points for contractive type multimaps involving the function where and the function is a -distance on a metric space Our results either generalize or improve several known fixed point results in the setting of metric spaces, (see Remarks 2.3 and 2.6).

We begin by presenting an integral formula involving the functions (31) and (32), which is asserted by the following lemma.

We notice that till now, most results in optimization theory were stated under generalized convexity assumptions involving the functions F which are sublinear.

Notably, individuals with schizophrenia and autism exhibit eye movement disturbances69,70, which may involve the function of the SC.

To investigate the possible oncogenic pathways that may involve the function of GNA13, western blotting was performed.

One of the most common forms of constraint involves the function of anatomical traits that differ in size.