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The distance between fixed points of some pairs of maps in Banach spaces and applications to differential systems

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Abstract

Let T be a λ-contraction on a Banach space Y and let S be an almost λ-contraction, i.e. sum of an (ε, λ)-contraction with a continuous, bounded function which is less than ε in norm. According to the contraction principle, there is a unique element u in Y for which u = Tu: If moreover there exists v in Y with v = Sv, then we will give estimates for ‖u−v‖. Finally, we establish some inequalities related to the Cauchy problem.

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Authors and Affiliations

  1. Dept. of Mathematics, Valahia University of Targoviste, Bd. Unirii 18, Targoviste, Romania

    Cristinel Mortici

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  1. Cristinel Mortici
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Mortici, C. The distance between fixed points of some pairs of maps in Banach spaces and applications to differential systems. Czech Math J 56, 689–695 (2006). https://doi.org/10.1007/s10587-006-0048-y

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  • DOI: https://doi.org/10.1007/s10587-006-0048-y

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