An Algorithm for Approximating Fixed Points Generalized Double Midpoint Rule

Subject Areas : Fixed Point Theory and its Applications

Hamid Sahebi ¹ (Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran)

Received: 2022-12-09 Accepted : 2022-12-14 Published : 2022-10-01

Keywords: Hilbert space, generalized double midpoint rule, asymptotically nonexpansive mapping, fixed point,

Abstract :

In this paper we introduce a new nonlinear algorithm for approximating xed points ofdouble midpoint rule on a nonempty, closed and convex subset of real Hilbert spaces. Undersome specic assumption imposed on the control parameters, we prove a strong convergencetheorem. In this manner, we provide some numerical examples to illustrate our main resultand to display the eciency of the proposed algorithm.