Inertial Extragradient Method for Solving Variational Inequality and Fixed Point Problems of a Bregman Demigeneralized Mapping in a Reflexive Banach Spaces
Hammed Anuoluwapo Abass, Godwin Chidi Ugwunnadi, Ojen Kumar Narain, Vahid Darvish
Abstract
In this paper, by employing a Bregman distance approach, we introduce a self-adaptive inertial extragradient method for finding a common solution of variational inequality problem involving a pseudo-monotone operator and fixed point problem of a Bregman demigeneralized mapping in a reflexive Banach spaces. Using a Bregman distance approach, we establish a strong convergence result for approximating the common solution of the aforementioned problems under some mild assumptions. We display some numerical examples to show the performance of our iterative method. The result presented in this paper extends and complements many related results in literature.
Topics & Concepts
Bregman divergenceMathematicsBanach spaceVariational inequalityFixed pointMonotone polygonPseudo-monotone operatorInertial frame of referenceConvergence (economics)Applied mathematicsOperator (biology)Iterative methodReflexivityMathematical optimizationMathematical analysisOperator spaceFinite-rank operatorGeometryBiochemistryRepressorChemistrySocial scienceTranscription factorEconomicsEconomic growthGeneSociologyQuantum mechanicsPhysicsOptimization and Variational AnalysisFixed Point Theorems AnalysisContact Mechanics and Variational Inequalities