Sentence examples for a manageable function from inspiring English sources

Since η is a manageable function, (0leqeta(a_{n},b_{n})< b_{n}-a_{n}) for all (ninmathbb{N}).

The same argument guarantees that ϱ, defined from (mathbb{R}times mathbb{R}) into (mathbb{R}), is not a manageable function.

If (kin 0,1)), then the function (eta:mathbb{R}timesmathbb{R}rightarrowmathbb{R}) given by (eta t,s)=k s-t) for all (t,sinmathbb{R}), is a manageable function, and its restriction to ([0,infty)tises[0,infty)) is a simulation function.

We denote the set of all manageable functions by (widehat{operatorname{Man}(mathsf{R})}).

We denote the sets of all manageable functions by Man ( R ) ˆ. Remark 2.1 If η ∈ Man ( R ) ˆ, then η ( t, t ) < 0 for all t > 0. Example 2.1 Let γ ∈ [ 0, 1 ) and a ≥ 0. Then the function η γ : R × R → R defined by η γ ( t, s ) = γ s − t − a is manageable. Example 2.2 ([12.2.

Every manageable function leads to a simple corollary considering the corresponding R-function.

The notion of manageable function was introduced in order to study multi-valued contractions.

And, in order to extend some results in the field of multi-valued maps, Du and Khojasteh presented the very close (but independent) notion of manageable function (see [14]).

Like (mathcal{Z} -contractions are based in manageable functions, the key piece of an R-contraction is its associated underlying R-function, which satisfies two independent conditions involving sequences of nonnegative real numbers.

Several examples of simulation functions and manageable functions can be found on [12 14].

Very recently, Du and Khojasteh [12] first introduced the concept of manageable functions.