Abstract
In this paper, we prove that a three-step iteration process is stable for contractive-like mappings. It is also proved analytically and numerically that the considered process converges faster than some remarkable iterative processes for contractive-like mappings. Furthermore, some convergence results are proved for the mappings satisfying Suzuki’s condition (C) in uniformly convex Banach spaces. A couple of nontrivial numerical examples are presented to support the main results and the visualization is showed by Matlab. Finally, by utilizing our main result the solution of a nonlinear fractional differential equation is approximated.
Highlights
Throughout this paper, Z+ denotes the set of all nonnegative integers
By using iteration process (1.7) we approximate the solution of a nonlinear fractional differential equation
7 Conclusion In this paper, convergence and stability of the JF iteration process have been studied for nonlinear mappings
Summary
Throughout this paper, Z+ denotes the set of all nonnegative integers. We assume that U is a nonempty subset of a Banach space W and F(F ) = {t ∈ U : F : U → U and F t = t}. Ali et al [2] introduced a new iteration process, called JF iteration process and approximated the fixed points of Hardy and Rogers generalized non-expansive mappings in uniformly convex Banach spaces. In this process, the sequence {τn} is generated by an initial guess τ0 ∈ U and defined as follows:. We prove some convergence results for Suzuki generalized non-expansive mappings via the JF iteration process in uniformly convex Banach spaces. Theorem 4.3 Assume that W satisfies Opial’s condition, the sequence {τn} developed by iteration process (1.7) converge weakly to a point of F(F ).
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