Strong Convergence Theorems for a Finite Family of Enriched Strictly Pseudocontractive Mappings and ΦT-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.

Strong and Weak Convergence Theorems for the Split Feasibility Problem of (β,k)-Enriched Strict Pseudocontractive Mappings with an Application in Hilbert Spaces

“…Remark 1. The class of β-enriched Lipschitz mappings is between the class of Lipschitz mappings and the class of (β, Φ Γ )-enriched Lipschitz mappings studied in [1]. (Recall that a nonlinear mapping Γ : K −→ K is called a (β, Φ Γ )-enriched Lipschitz mapping (or Φ Γ -enriched Lipschitzian) if for all ϱ, ω ∈ K, there exist β ∈ [0, +∞) and a continuous nondecreasing function Φ Γ : R + −→ R + , with Φ(0) = 0, such that ∥β(ϱ − ω) + Γϱ − Γω∥ ≤ (β + 1)Φ Γ (∥ϱ − ω∥).)…”

On Neutrosophic 2-Metric Spaces with Application

“…Al-Omeri et al [21] worked on (Φ, Ψ)-weak contractions in the context of neutrosophic cone metric spaces. Naeem et al [22] worked on strong convergence theorems for a finite family of enriched strictly pseudocontractive mappings and Φ T -enriched Lipschitzian mappings using a new modified mixed-type Ishikawa iteration scheme with error. Al-Omeri et al [23,24] worked on numerous interesting contraction mappings in the context of neutrosophic cone metric spaces.…”

Existence Results for Wardoski-Type Convex Contractions and the Theory of Iterated Function Systems

“…Now, we should recall that symmetry is a mapping on some object X, which is supposed to be structured onto itself such that the structure is preserved. Saleem et al [18] and Sain [19] provided several ways this mapping could occur. Neugebaner [17], using the concept of symmetry, obtained several applications of a layered compression-expansion fixed-point theorem in the existence of solutions of a second-order difference equation with Dirichlet boundary conditions.…”