An iterative method for (AGDDV I P) in Hilbert space and the Homology theory to study the (GDDC$P _n$) in Riemannian n-manifolds in the presence of fixed point inclusion

Abstract

The main purpose of this paper is to study the convergence of variable step iterative methods for the defined problem absolutely generalized dominated differential variational inequality problems (AGDDV I P) in Hilbert spaces. The iterative process considered in the paper admit the presence of variable iteration parameters, which can be useful in numerical implementation to find solution of the problem (AGDDV I P). Finally, we study the existence theorems of the problems (GDDVI$P _n$) and (GDDC$P _n$) in Riemannian n-manifolds modelled on the Hilbert space in the presence of coincidence index, fixed point theorem of Homology theory and one-point compactification of Topology theory. 2000 Mathematics Subject Classifications: 65K10; 90C33; 47J30