Sentence examples for mappings and arbitrary from inspiring English sources

Henceforth, for any given finite family ({T_{i}, i=1,ldots,m}) of generalized (k_{i} -strictly pseudo-contractive multi-valued mappings and arbitrary sequence ({x_{n}}subseteq k_{i} -strictlyi}:= biggl{ y_{n}^{i}in T_{i}x_{n}:D^{2}bigl({x_{n}}, T_{i}x_{n}bigr)leqbiglVert x_{n}-y_{n}^{i} bigrVert ^{2}+frac{1}{n^{2}} biggr}.

In [14], the authors introduced the following notions in which (F,H Xtimes Xrightarrow X) are two arbitrary mappings, and they proved the following theorem.

Let a, N, V, Y be defined as in Lemma  2.4, let (f : V to Y) and (F : V to Y) be arbitrary mappings, and let n be a fixed integer greater than 1.

Let (k neq1), b, V, Y be as in Lemma  2.2, let (f : V to Y) and (F : V to Y) be arbitrary mappings, and let n be a fixed integer greater than 1.

The high detection rate of violations of the arbitrary sensorimotor mappings and the activation of a distributed parietofrontal network during observation of the instruction cues and subsequent movements (Fig. 5) suggest that the observed actions induced first-person sensorimotor processes.

In this section, we study the rate of convergence of W(T,N -iteration and K(T,N -iteration for continuous and nondecreasing mappings on an arbitrary interval in the sense of Rhoades.

Moreover, they present the solvability of variational-like inequalities with relaxed η-α monotone mappings in arbitrary Banach spaces (see also in [2, 15 20] and [23 28]).

They're arbitrary constants, arbitrary variables, and arbitrary expressions.

It sounds frivolous and arbitrary.

The government had grown corrupt and arbitrary.

That is both too simplistic and arbitrary.