2014/03/13 by İbrahim Karahan, Karahan, Ibrahim, Murat Özdemir +1
Computer Science · Engineering · Mathematics · #47H09 #47J20 #49J30 #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Optimization and Variational Analysis #Topology Optimization in Engineering
paper · pdf · doi:10.48550/arxiv.1403.3390
openalex publication_date 2014/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an inverse strongly monotone mapping in a real Hilbert space. Also, we prove that under quite mild conditions the iterative sequence defined by our new extragradient method converges strongly to a solution of the fixed point problem for an infinite family of nonexpansive mappings and the classical variational inequality problem. In addition, utilizing this result, we provide some applications of the considered problem not just giving a pure extension of existing mathematical problems.