Abstract
We introduce a new contractive condition and a new iterative method in n0normed space setting. We employ both of these to study convergence, stability, and data dependence. The results presented here extend and improve some recent results announced in the existing literature.
Highlights
The theory of n-normed spaces has been introduced by Misiak [1] as a generalization of the theory of 2-normed spaces due to Gähler [2]
We introduce a new contractive condition and a new iterative method in n normed space setting
Much e¤ort has been devoted to the development of the theory of n normed spaces
Summary
The theory of n-normed spaces has been introduced by Misiak [1] as a generalization of the theory of 2-normed spaces due to Gähler [2]. Dutta [3] introduced a generalized Z-type contractive condition as follows: Let K be nonempty, closed, convex subset of real linear n normed space X and T : K ! In [3], some convergence results have been constructed for ...xed point of the mappings satisfying condition (6) via iterative schemes (1.1), (1.2) and (1.3). We introduce the following contractive condition: Let (X; k ; : : : ; k) be an n normed space, T : X ! We ...rst prove some convergence results for the mappings satisfying condition (7) via iterative methods (1.4) and (5).
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