Iterative algorithm for zeros of maximal monotone mappings in uniformly smooth and uniformly convex Banach spaces

Let E be a uniformly smooth and uniformly convex real Banach space and $E^*$ be its dual space. Let $A : E \rightarrow E^*$ be a bounded maximal monotone mappping such that $A^{-1}(0) \ne 0$. Define the algorithm $\{x_n\}$ as follows: for given $x_1 \in E$,\;\; $x_{n+1}= J^{-1}\big(Jx_n-\lambda_nAx_n-\lambda_n\theta_n (Jx_n-Jx_1)\big)$ where $J$ is the normalized duality mapping from $E$ into $E^*$ and $ \{\lambda_n \}$ and $ \theta_n $ are positive real numbers in $(0, 1)$ satisfying suitable conditions. It is proved that $x_n$ converges strongly to some $x^*\in A^{-1}(0)$. The results extend our recent works \cite{mendy-et-al} to larger class of Banach spaces with numerical simulations.