Quasi-nonexpansive mappings with respect to orbits in Banach spaces and weak fixed point property

Subject Areas : Functional analysis

K. Fallahi ¹ , H. Ardakani ² , F. Norouzi ³

1 - Javanroud Faculty of Management and Accounting, Razi University, Kermanshah, Iran
2 - Department of Mathematics, Payame Noor University, P.O. BOX 19395-3697, Tehran, Iran
3 - Department of Mathematics, Payame Noor University, P.O. BOX 19395-3697, Tehran, Iran

Received: 2024-08-25 Accepted : 2024-12-06 Published : 2024-12-07

Keywords: Fixed point property, normal structure, nonexpansive mappings,

Abstract :

In the present work, we introduce quasi-nonexpansive mappings with respect to orbits on the Banach space. Then we show that a Banach space $\mathcal{A}$ has weak normal structure if and only if $\mathcal{A}$ has the weak fixed point property for quasi-nonexpansive mappings with respect to orbits.

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