Multi-step iterative algorithm for minimization and fixed point problems in p-uniformly convex metric spaces

Abstract

In this paper, we propose and study a multi-step iterative algorithm that comprises of a finite family of asymptotically \begin{document}$ k_i $\end{document} -strictly pseudocontractive mappings with respect to \begin{document}$ p, $\end{document} and a \begin{document}$ p $\end{document} -resolvent operator associated with a proper convex and lower semicontinuous function in a \begin{document}$ p $\end{document} -uniformly convex metric space. Also, we establish the \begin{document}$ \Delta $\end{document} -convergence of the proposed algorithm to a common fixed point of finite family of asymptotically \begin{document}$ k_i $\end{document} -strictly pseudocontractive mappings which is also a minimizer of a proper convex and lower semicontinuous function. Furthermore, nontrivial numerical examples of our algorithm are given to show its applicability. Our results complement a host of recent results in literature.