### Sequences of ϕ-contractions and convergence of fixed points

#### Abstract

Given a metric space (X,d) and, for each n=1,2,..., let T_{n}:X_{n}→X_{n} be a mapping with fixed point x_{n}, where {X_{n}} is a sequence of nonempty subsets of X. Assume that each mapping T_{n} is a ϕ-contraction with respect to a different metric d_{n}. In this paper conditions are obtained under which the convergence of the sequence {T_{n}} in some general sense to a limit mapping implies the convergence of the sequence of their fixed points {x_{n}}. This leads to a number of new stability results which generalize certain well-known results.

**How to Cite this Article:**S. N. Mishra, S. L. Singh, Rajendra Pant, Sequences of ϕ-contractions and convergence of fixed points, Adv. Fixed Point Theory, 3 (2013), 60-69 Copyright © 2013 S. N. Mishra, S. L. Singh, Rajendra Pant. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Advances in Fixed Point Theory

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