Sentence examples for a class of auxiliary from inspiring English sources

In particular, amacrine cells of the vertebrate retina make a class of auxiliary cells expressing various neurotransmitters, such as GABA, glycine, serotonin (5-HT), but also dopamine (DA) [ 1].

We introduce and study a new class of auxiliary problems for solving the equilibrium problem in Banach spaces.

Following the first line of research, in recent times, Khojasteh et al. [18] introduced the notion of (mathcal{Z} -contraction by using a new class of auxiliary functions called simulation functions.

In 1973, Geraghty [33] introduced an interesting class of auxiliary functions to refine the Banach contraction mapping principle.

(1.9) is a class of most important auxiliary equations because many nonlinear evolution equations can be converted to this equation making use of the traveling wave reduction.

Hence, ϕ belongs to a more general class of auxiliary functions.

Lim characterized this kind of mappings in terms of a contractivity condition using the following class of auxiliary functions.

Now, we define the following class of auxiliary functions which will be used densely in the sequel.

For our aim, we need to define the following class of auxiliary mappings: Let Λ be set of functions (varphi: [0,+infty)rightarrow [0,+infty)) such that (varphi^{-1}({0})={0}): begin{aligned}& Psi ={psiinLambdavertpsitext{ is continuous, non-decreasing} }quad text{and} & Phi ={phiinLambda vert phitext{ is lower semi-continuous} }. end{aligned} Let ((X,q)) be a quasi-partial metric space.

Consider also a class of so-called primary (i.e., auxiliary) self-maps, for all to be used to build the class of maps under study through Fixed Point Theory which is defined by (2.1).

The proposed H∞-control problem for a class of linear systems with time-delays is realized as an H∞-control problem for an auxiliary linear system free of time-delay.