A viscosity iterative algorithm for a family of monotone inclusion problems in an Hadamard space
Grace Nnennaya Ogwo, Chinedu Izuchukwu, Kazeem Olalekan Aremu, Oluwatosin Temitope Mewomo
Abstract
In this paper, we introduce a viscosity-type proximal point algorithm which comprises of a finite sum of resolvents of monotone operators, and a generalized asymptotically nonexpansive mapping. We prove that the algorithm converges strongly to a common zero of a finite family of monotone operators, which is also a fixed point of a generalized asymptotically nonexpansive mapping in an Hadamard space. Furthermore, we give two numerical examples of our algorithm in finite dimensional spaces of real numbers and one numerical example in a non-Hilbert space setting, in order to show the applicability of our results.
Topics & Concepts
MathematicsMonotone polygonHilbert spaceHadamard transformFixed pointSpace (punctuation)Strongly monotoneApplied mathematicsViscosityAlgorithmPure mathematicsDiscrete mathematicsMathematical analysisComputer scienceGeometryOperating systemPhysicsQuantum mechanicsOptimization and Variational AnalysisNonlinear Differential Equations AnalysisAdvanced Optimization Algorithms Research