New Four-Step Iteration in Convex Metric Spaces
Keywords:
Convex metric space, quasi nonexpansive, Κ-contraction, Fajer monotone Κ-nonexpansive.Abstract
In this paper, we introduce a new four-step iterative process in convex metric spaces for approximating fixed points of nonlinear mappings. The proposed iterative scheme is studied for two important classes of mappings, namely fundamentally nonexpansive mappings and conditional quasi-contractive mappings. We establish the existence of fixed points and prove strong convergence theorems for the proposed algorithm under appropriate assumptions. Moreover, we show that the generated iterative sequence is Fejér monotone in convex partial metric spaces, which plays a key role in the convergence analysis. To demonstrate the efficiency of the proposed method, several numerical examples and comparison patterns are presented. The convergence rate of the new iterative process is compared with existing iterative algorithms by using the standard definition of faster convergence, showing that the proposed method converges more rapidly than the considered iterative schemes. in this paper introduced a new iterative in convexity in metric spaces using Fundamentally nonexpansive and conditional quasi contractive and Ferer monotone sequence in convex partial metric space, also prove the existence and convergence theorems for the fixed point and use different patterns for comparison
using the definition of the faster.
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