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GeneralizedI-nonexpansive maps and invariant approximation results inp-normed spaces

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Abstract

We extend the concept of R-subcommuting maps due to Shahzad[17,18] to the case of non-starshaped domain and obtain a common fixed point result for this class of maps on non-starshaped domain in the setup of p-normed spaces. As applications, we establish noncommutative versions of various best approximation results for generalized I-nonexpansive maps on non-starshaped domain. Our results unify and extend that of Al-Thagafi, Dotson, Habiniak, Jungck and Sessa, Latif, Sahab, Khan and Sessa and Shahzad.

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Hussain, N. GeneralizedI-nonexpansive maps and invariant approximation results inp-normed spaces. Analysis in Theory and Applications 22, 72–80 (2006). https://doi.org/10.1007/BF03218700

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Key words

  • common fixed point
  • contractive family of functions
  • R-subcommuting maps
  • invariant approximation

AMS(2000) subject classification

  • 47H10
  • 54H25