An iiterative method for t-η-invex function in hubert space and coincidence lifting index theorem for lifting function and covering maps

摘要

The main purpose of this paper is to study the convergence of variable step iterative methods for T-η-invex function in Hubert spaces. The iterative process considered in the paper admit the presence of variable iteration parameters, which can be useful in numerical implementation to find T-η-invex function. We defined and study the generalized dominated differential variational inequality problems (GDDVIP) in reflexive real Banach spaces as an extension of T-η-invex function. We define the generalized dominated differential vector variational inequality problems (GDDVVIP)x and the generalized dominated differential vector complementarity problems (GDDVCP)x in H-differentiable manifolds. We introduce the coincidence lifting index lemma and using this lemma we study the coincidence lifting index theorem of lifting function and covering maps in Riemannian n-manifolds in the presence of homotopy function and fixed-point index of a function.