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In this paper, the concept of a generalized almost (f,g)-contraction is introduced and we establish some common fixed-point results for the noncommuting generalized almost (f,g)-contraction in the setup of metric spaces and normed linear spaces, where the set of fixed points of f and g need not be starshaped. As applications, invariant approximation results are proved. Supporting examples are also given.

Some common fixed-point and invariant approximation results with generalized almost contractions