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We prove convergence theorems of the modified S-iteration generated by a pair of single-valued asymptotically nonexpansive tand multi-valued nonexpansive mappings Tin Banach spaces. An example was constructed to prove the novelty of our results.

We describe a new deep learning model - Convolutional eXtreme Gradient Boosting (ConvXGB) for classification problems based on convolutional neural nets and Chen et al.’s XGBoost. As well as image data, ConvXGB also supports the general classification problems, with a data preprocessing module. ConvXGB consists of several stacked convolutional layers to learn the features of the input and is able to learn features automatically, followed by XGBoost in the last layer for predicting the class labels. The ConvXGB model is simplified by reducing the number of parameters under appropriate conditions, since it is not necessary re-adjust the weight values in a back propagation cycle. Experiments on several data sets from UCL Repository, including images and general data sets, showed that our model handled the classification problems, for all the tested data sets, slightly better than CNN and XGBoost alone and was sometimes significantly better.

In this paper, we study the split common fixed point problem in Hilbert spaces. We find a common solution of the split common fixed point problem for two demicontractive operators without a prioriknowledge of operator norms. A strong convergence theorem is obtained under some additional conditions and numerical examples are included to illustrate the applications in signal compressed sensing and image restoration.