We introduce a new iterative scheme for finding the common element of the set of common fixed points of nonexpansive mappings, the set of solutions of an equilibrium problem, and the set of solutions of the variational inequality. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. Moreover, we apply our result to the problem of finding a common fixed point of a countable family of nonexpansive mappings, and the problem of finding a zero of a monotone operator. This main theorem extends a recent result of Yao et al. (2007) and many others.

The purpose of this paper is to study the strong convergence theorems of Moudafi’s viscosity approximation methods for a nonexpansive mapping T in CAT(0) spaces without the property . For a contraction f on C and t ∈ ( 0 , 1 ) , let x t ∈ C be the unique fixed point of the contraction x ↦ t f ( x ) ⊕ ( 1 − t ) T x ; i.e.,

The use of photovoltaic systems has increased in recent years due to their decreasing costs and improved performance. However, these systems can be susceptible to faults that can reduce efficiency and energy yield. To prevent and reduce these problems, preventive or predictive maintenance and effective monitoring are necessary. PV health monitoring systems and automatic fault detection and diagnosis methods are critical for ensuring PV plants’ reliability, high-efficiency operation, and safety. This paper presents a new framework for developing fault detection in photovoltaic (PV) systems. The proposed approach uses machine learning algorithms to predict energy power production and detect anomalies in PV plants by comparing the predicted power from a model and the measured power from sensors. The framework utilizes historical data to train the prediction model, and live data is compared with predicted values to analyze residuals and detect abnormal scenarios. The proposed approach has been shown to accurately distinguish anomalies using constructed thresholding, either static or dynamic thresholds. The paper also reports experimental results using the Matthews correlation coefficient, a more reliable statistical rate for an imbalanced dataset. The proposed approach leads to a reasonable anomaly detection rate, with an MCC of 0.736 and a balanced ACC of 0.863.

We introduce a novel twin support vector machine with the generalized pinball loss function (GPin-TSVM) for solving data classification problems that are less sensitive to noise and preserve the sparsity of the solution. In addition, we use a symmetric kernel trick to enlarge GPin-TSVM to nonlinear classification problems. The developed approach is tested on numerous UCI benchmark datasets, as well as synthetic datasets in the experiments. The comparisons demonstrate that our proposed algorithm outperforms existing classifiers in terms of accuracy. Furthermore, this employed approach in handwritten digit recognition applications is examined, and the automatic feature extractor employs a convolution neural network.