Frum-Ketkov type multivalued operators

Karapinar, Erdal, Petruşel, Adrian and Petruşel, Gabriela

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carpathian_2021_37_2_203_210

Issue no: Vol 37/2021 no. 2 Tags: asymptotic regular selection, fixed point structure, Frum-Ketkov operator, Fixed point, asymptotic regular multivalued operator, Metric space, contractive multivalued operator, Multivalued weakly Picard operator, quasinonexpansive multivalued operator, Strict fixed point, strong Frum-Ketkov multivalued operator, asymptotic regularity, Frum-Ketkov selection

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Let $(M,d)$ be a metric space, $X\subset M$ be a nonempty closed subset and $K\subset M$ be a nonempty compact subset. By definition, an upper semi-continuous multivalued operator $F:X\to P(X)$ is said to be a strong Frum-Ketkov type operator if there exists $\alpha\in ]0,1[$ such that $e_d(F(x),K)\le \alpha D_d(x,K)$ , for every $x\in X$ , where $e_d$ is the excess functional generated by $d$ and $D_d$ is the distance from a point to a set. In this paper, we will study the fixed points of strong Frum-Ketkov type multivalued operators.