On Two Fixed Point Properties of Mean Non-expansive Mappings

Firstly, the result of theorem 5.10 in reference ［1］ is extended to a more general form of mapping, namely: sup(y∈E)≤‖Tx－Ty‖≤sup(y∈E)(a‖x－y‖+b‖x－Tx‖+c‖x－Ty‖)，x∈K，a,b,c≥0，a+b+c≤1, and it is proved that there are fixed points for this kind of mapping which is from bounded closed convex subset K with normal structure of a reflexive Banach space into itself. Moreover, in convex b-metric space, it is proved that there is a unique fixed point for the mean non-expansive mapping under certain conditions by utilizing the sequence which is generated by Mann iteration.

Abstract licence: CC BY

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