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In this paper, we introduce a commutative mappings satisfying the class ofgeneralized non-expansive mappings which is wider than the class of mappingssatisfying the condition (C), so called Condition B gamma, mu. The resultsobtained in this paper extend and generalized non-expansive mappings and otherresults in this direction. Different properties and some fixed point resultsfor the mappings are obtained here.  Keywords: Non expansive mappings, Condition (C), Condition B gamma mu,Commuting mappings, Fixed point.

Existence and convergence of commutative mappings on some results of fixed point theory in a class of generalized non-expansive mappings