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

In this paper, we introduce a commutative mappings satisfying the class of generalized non-expansive mappings which is wider than the class of mappings satisfying the condition ©, so called Condition B gamma, mu. The results obtained in this paper extend and generalized non-expansive mappings and other results in this direction. Different properties and some fixed point results for the mappings are obtained here. Keywords: Non expansive mappings, Condition ©, Condition B gamma mu, Commuting mappings, Fixed point.