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The MnO2-based heterogeneous catalyst has been considered as one of the most efficient catalysts for enzyme-like catalysis, however, it usually suffers from low stability and difficulty in recycling and reuse. Herein, MnO2 nanosheets supported on nickel foam (NF@MnO2) have been fabricated, via a facile one-step hydrothermal process, as an artificial oxidase for the detection and quantification of ascorbic acid (AA). NF, as a magnetic support, possesses a three-dimensional (3D) skeleton and excellent conductivity, which greatly facilitate the utilization of active sites, electron transfer, as well as separation from the solution with an external magnet. Owing to this unique architecture and the synergistic effect between NF and MnO2, the designed NF@MnO2 composites show enhanced enzyme-like activity toward the oxidation of 3,3′,5,5′-tetramethylbenzidine (TMB) as compared to NF or MnO2 alone. By virtue of the reducing ability of ascorbic acid (AA), the AA selectively inhibited this reaction with a detection limit of 0.1 μM. More importantly, this kind of NF-based design can be easily extended to the synthesis of other functional materials for enzyme-like catalytic applications. [ABSTRACT FROM AUTHOR]

We introduce two new concepts of weakly relaxed η-α monotone mappings and weakly relaxed η-α semimonotone mappings. Using the KKM technique, the existence of solutions for variational-like problems with weakly relaxed η-α monotone mapping in reflexive Banach spaces is established. Also, we obtain the existence of solution for variational-like problems with weakly relaxed η-α semimonotone mappings in arbitrary Banach spaces by using the Kakutani-Fan-Glicksberg fixed-point theorem. [ABSTRACT FROM AUTHOR]

We introduce the concept of the generalized wα-contraction mappings and establish the existence of fixed point theorem for such mappings by using the properties of w-distance and α-admissible mappings. We also apply our result to coincidence point and common fixed point theorems in metric spaces. Further, the fixed point theorems endowed with an arbitrary binary relation are also derived from our results. Our results generalize the result of Kutbi, 2013, and several results in the literature. [ABSTRACT FROM AUTHOR]