
In this paper, a sufficient and necessary condition for the convergence of the sequence of successive \(\{T^n x\}\) approximations to a fixed point of self mapping \(T\) on a complete metric space \((X, d)\) is given. Some equivalent conditions for the convergence of the sequence of successive \(\{T^n x\}\) approximations to a unique fixed point of self mapping \(T\) on a complete metric space \((X, d)\) are also given.
\(\tau \)-distance, fixed point, Fixed-point and coincidence theorems (topological aspects), the Banach contraction principle, successive approximations, Subrahmanyam's fixed point theorem, strong leader mapping
\(\tau \)-distance, fixed point, Fixed-point and coincidence theorems (topological aspects), the Banach contraction principle, successive approximations, Subrahmanyam's fixed point theorem, strong leader mapping
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