One-step growth of Cu-doped carbon dots in amino-modified carbon nanotube-modified electrodes for sensitive electrochemical detection of BPA.

Copper-doped carbon dots and aminated carbon nanotubes (Cu-CDs/NH2-CNTs) nanocomposites were synthesized by a one-step growth method, and the composites were characterized for their performance. An electrochemical sensor for sensitive detection of bisphenol A (BPA) was developed for using Cu-CDs/NH2-CNTs nanocomposites modified with glassy carbon electrodes (GCE). The sensor exhibited an excellent electrochemical response to BPA in 0.2 M PBS (pH 7.0) under optimally selected conditions. The linear range of the sensor for BPA detection was 0.5-160 µM, and the detection limit (S/N = 3) was 0.13 µM. Moreover, the sensor has good interference immunity, stability and reproducibility. In addition, the feasibility of the practical application of the sensor was demonstrated by the detection of BPA in bottled drinking water and Liu Yang River water.

Multivariate systems of nonexpansive operator equations and iterative algorithms for solving them in uniformly convex and uniformly smooth Banach spaces with applications.

We prove some existence theorems for solutions of a certain system of multivariate nonexpansive operator equations and calculate the solutions by using the generalized Mann and Halpern iterative algorithms in uniformly convex and uniformly smooth Banach spaces. The results of this paper improve and extend the previously known ones in the literature.

A kind of system of multivariate variational inequalities and the existence theorem of solutions.

Let K be a nonempty closed convex and bounded subset of a reflexive Banach space X. Let [Formula: see text] be N-variables monotone demi-continuous mappings from [Formula: see text] into X. Then: (1) the system of multivariate variational inequalities [Formula: see text] has a solution [Formula: see text]; (2) the set of solutions of this system of multivariate variational inequalities is closed convex in [Formula: see text]; (3) if [Formula: see text] are also strictly monotone, this system of multivariate variational inequalities has a unique solution.

ψ-Contraction and [Formula: see text]-contraction in Menger probabilistic metric space.

The purpose of this paper is to present the definition of [Formula: see text]-contractive mapping and to discuss the relation of [Formula: see text]-contractive mappings and [Formula: see text]-contractive mappings. Furthermore, the generalized [Formula: see text]-contraction mapping principle has been proved without the uniqueness condition. Meanwhile, the generalized [Formula: see text]-contraction mapping principle has been obtained by using an ingenious method.