O. T. Mewomo | Searcharxiv

arXiv2021

On generalized Φ-strongly monotone mappings and algorithms for the solution of equations of Hammerstein type

In this paper, we consider the class of generalized Φ-strongly monotone mappings and the methods of approximating a solution of equations of Hammerstein type. Auxiliary mapping is defined for nonlinear integral equations of Hammerstein type. The auxiliary mapping is the composition of bounded generalized Φ-strongly monotone mappings which satisfy the range condition. Suitable conditions are imposed to obtain the boundedness and to show that the auxiliary mapping is a generalized Φ-strongly which satisfies the range condition. A sequence is constructed and it is shown that it converges strongly to a solution of equations of Hammerstein type. The results in this paper improve and extend some recent corresponding results on the approximation of a solution of equations of Hammerstein type.

math.FA↗

arXiv2020

Strong convergence theorems for strongly monotone mappings in Banach spaces

Let $E$ be a uniformly smooth and uniformly convex real Banach space and $E^*$ be its dual space. Suppose $A : E\rightarrow E^*$ is bounded, strongly monotone and satisfies the range condition such that $A^{-1}(0)\neq \emptyset$. Inspired by Alber [2], we introduce Lyapunov functions and use the new geometric properties of Banach spaces to show the strong convergence of an iterative algorithm to the solution of $Ax=0$.

math.FA↗