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This paper presents and analyzes a new viscosity approximation method with the inertial technique for finding a common fixed point of a countable family of nonexpansive mappings and then its strong convergence theorem is established under some suitable conditions. As a consequence, we employ our proposed algorithm for solving some convex bilevel optimization problems and then apply it for solving regression of a graph of cosine function and classification of some noncommunicable diseases by using the extreme learning machine model. We perform a comparative analysis with other algorithms to demonstrate the performance of our approach. Our numerical experiments confirm that our proposed algorithm outperforms other methods in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new inertial iterative algorithm involving the linesearch rule for the split variational inclusion in real Hilbert spaces. We use two inertial terms to accelerate the convergence speed of the proposed algorithm. Under suitable conditions, we prove its weak convergence theorem. Finally, in applications, we apply our algorithm to image deblurring and data classification problem in predicting diabetes mellitus. [ABSTRACT FROM AUTHOR]

In this paper, the existence of best proximity point theorems for two new types of nonlinear non-self mappings in a complete metric space endowed with a directed graph are established. Our main results extend and generalize many known results in the literatures. As a special case of the main results, the best proximity point theorems on partially ordered sets are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point theorems for non-self G-almost contractive mappings in Banach spaces with a directed graph and give some examples to illustrate our main results. The main results in this paper extend and generalize many known results in the literature therein. [ABSTRACT FROM AUTHOR]