Strong Convergence Theorems for a Finite Family of Enriched Strictly Pseudocontractive Mappings and Φ_<i>T</i>-Enriched Lipschitizian Mappings Using a New Modified Mixed-Type Ishikawa Iteration Scheme with Error

Abstract

In this paper, we introduce two new classes of mappings known as λ-enriched strictly pseudocontractive mappings and ΦT-enriched Lipshitizian mappings in the setup of a real Banach space. In addition, a new modified mixed-type Ishikawa iteration scheme was constructed, and it was proved that our iteration method converges strongly to the common fixed points of finite families of the above mappings in the framework of a real uniformly convex Banach space. Moreover, we provided a non-trivial example to support our main result. Our results extend and generalize several results existing in the literature.

Keywords

• finite family
• enriched strictly pseudocontractive mapping
• Φ_<i>T</i>-enriched Lipschitizian self-mapping
• modified Ishikawa mixed-type iteration scheme
• common fixed point
• uniformly convex Banach space