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Noncommuting maps and invariant approximations

Hussain N., Latif A., Al-Mezel S.

Demonstratio Mathematica

2007

Vol. 40, nr 4

895-905

We obtain common fixed point results for generalized I-nonexpansive compatible as well as weakly compatible maps. As applications, various best approximation results for this class of maps are derived in the setup of certain metrizable topological vector spaces.

Common fixed point and invariant approximation results

Hussain N.

Demonstratio Mathematica

2006

Vol. 39, nr 2

389-400

We extend the concept of R-subweakly commuting maps due to Shahzad [21] to the case of non-starshaped domain and obtain common fixed point results for this class of maps on non-starshaped domain in the setup of p-normed spaces. As applications, we establish Brosowski-Meinardus type approximation theorems. Our results unify and extend the results of Al-Thagafi, Dotson, Habiniak, Jungck and Sessa, Sahab, Khan and Sessa, Singh and Shahzad.