A new modified mixed-type Ishikawa iteration scheme with error for common fixed points of enriched strictly pseudocontractive self mappings and ΦΓ-enriched Lipschitzian self mappings in uniformly convex Banach spaces

Abstract

Let E be a uniformly convex Banach space and C a nonempty closed bounded convex subset of E. Let Γ : C ⟶ C and G : C ⟶ C be enriched strictly pseudocontractive mapping and Φ Γ -enriched Lipschitzian mapping respectively. We introduce the above two mappings in uniformly convex Banach space and thereafter prove that a new modified mixed-type lshikawa iteration scheme converges strongly to the common fixed points of Γ and G. In addition, we incorporate error terms to enhance the convergence of the method and also to improve the stability and robustness of the method. Our results extend and generalize the results obtained in [5] and so many other recent results currently existing in literature.

Keywords

• enriched strictly pseudocontractive mapping
• $\phi_{\gamma}$-enriched lipschitzian self mapping
• modified lshikawa mixed type iteration scheme
• common fixed point
• uniformly convex banach space
• strong convergence