Showing papers by "Chinedu Izuchukwu published in 2023"
TL;DR: In this paper , the authors studied the split feasibility and fixed point problem with multiple output sets in real Hilbert spaces and proposed two relaxed extragradient algorithms for finding approximate solutions to this problem and proved that the sequences they generate converge strongly.
Abstract: We study the split feasibility and fixed point problem with multiple output sets in real Hilbert spaces. Using Tikhonov's regularization and viscosity approximation techniques, we propose two relaxed extragradient algorithms for finding approximate solutions to this problem and prove that the sequences they generate converge strongly. Finally, we give some consequences and an application of our results, and also present numerical examples to validate the efficiency of our algorithms.
1 citations
TL;DR: In this paper , two Bregman projection methods for solving variational inequality problems in real reflexive Banach spaces were proposed. But they require only one projection onto the feasible set and one evaluation of the cost operator at each iteration.
Abstract: We study two Bregman projection methods for solving variational inequality problems in real reflexive Banach spaces. Our methods have simple and elegant structures, and they require only one Bregman projection onto the feasible set and one evaluation of the cost operator at each iteration. We prove that these methods converge weakly when the cost operator is pseudomonotone on the entire space and that they converge strongly when the cost operator is strongly pseudomonotone only on the feasible set. Extensions of our proposed methods to mixed variational inequality problems are also given. Finally, we consider some examples regarding the implementation of our methods in comparisons with known methods in the literature.
1 citations
TL;DR: In this paper , a modification of the Malitsky-Tam forward-reflected-backward splitting method with two-step inertial extrapolation was proposed to solve nonconvex mixed variational inequalities.
TL;DR: In this paper , a proximal point type of viscosity iterative method with double implicit midpoint rule comprising of a nonexpansive mapping and the resolvents of a monotone operator and a bifunction is introduced.
Abstract: Abstract In this paper, we introduce a proximal point-type of viscosity iterative method with double implicit midpoint rule comprising of a nonexpansive mapping and the resolvents of a monotone operator and a bifunction. Furthermore, we establish that the sequence generated by our proposed algorithm converges strongly to an element in the intersection of the solution sets of monotone inclusion problem, equilibrium problem and fixed point problem for a nonexpansive mapping in complete CAT(0) spaces. In addition, we give a numerical example of our method each in a finite dimensional Euclidean space and a non-Hilbert space setting to show the applicability of our method . Our results complement many recent results in the literature.
TL;DR: In this paper , the authors established a relationship between asymptotic regularity and common stationary points of multivalued mappings on a metric space, and obtained a new common fixed point result for two asymPTotically regular single-valued mappings.
Abstract: Abstract We establish a relationship between asymptotic regularity and common stationary points of multivalued mappings on a metric space. As a consequence of our results, we obtain a new common fixed point result for two asymptotically regular single-valued mappings. Our work significantly improves and complements comparable results in the literature.