Abstract

In this article, an inertial Mann-type iterative algorithm is constructed using the so-called viscosity method of A. Moudafi, Viscosity approximation methods for fixed-point problems, J. Math. Anal. Appl. {241(1)} (2000), 46--55. A strong convergence theorem of mean ergodic-type is proved using the sequence of the iterative algorithm for finding zeros of monotone mappings and the fixed point of a strict pseudo nonspreading mapping in a real Hilbert space. Finally, we apply our result to solve some minimization problem.

Keywords: Monotone operators; strict-pseudo contractive mappings; strict-pseudo nonspreading mappings; resolvents; Hilbert space.

MSC: 47H04, 47H06, 47H15, 47H17, 47J25

Pages:  89--100     

Volume  74 ,  Issue  2 ,  2022