On behaviour of holomorphically contractible systems under non-monotonic sequences of sets

The new results concerning the continuity of holomorphically contractible systems treated as set functions with respect to non-monotonic sequences of sets are given. In particular, continuity properties of Kobayashi and Carath\'eodory pseudodistances, as well as Lempert and Green functions with respect to sequences of domains converging in Hausdorff metric are delivered.Comment: 6 page

ROUGH CONTINUOUS CONVERGENCE OF SEQUENCES OF SETS

In this paper, we define a new type of convergence of sequences of sets by using the continuous convergence (or α-convergence) of the sequence of distance functions. Then we proved in which case it is equivalent to rough Wijsman convergence by considering the different values of the roughness degrees

Quasi-almost convergence of sequences of sets

In this paper, we defined concepts of Wijsman quasi-almost convergence and Wijsman quasi-almost statistically convergence. Also we give the concepts of Wijsman quasi-strongly almost convergence and Wijsman quasi q-strongly almost convergence. Then, we study relationship among these concepts. Furthermore, we investigate relationship between these concepts and some convergence types given earlier for consequences of sets, as wel

Lacunary statistical convergence of sequences of sets

Several notions of convergence for subsets of metric space appear in the literature. In this paper we define lacunary statistical convergence for sequences of sets and study in detail the relationship between other convergence concept

Lacunary statistical summability of sequences of sets

In this paper we define the WS_θ-analog of the Cauchy criterion for convergence and show that it is equivalent to Wijsman lacunary statistical convergence. Also, Wijsman lacunary statistical convergence is compared to other summability methods which are defined in this paper. After giving new definitions for convergence, we prove a result comparing them. In addition, we give the relationship between Wijsman lacunary statistical convergence and Hausdorf lacunary statistical convergenc

I-Cesàro summability of sequences of sets

In this paper, we defined concept of Wijsman I-Cesàro summability for sequences of sets and investigate the relationships between the concepts of Wijsman strongly I-Cesàro summability, Wijsman strongly I-lacunary summability, Wijsman p-strongly I-Cesàro summability and Wijsman I-statistical convergenc

Cesaro summability of double sequences of sets

In this paper, we study the concepts of Wijsman Ces`aro summability and Wijsman lacunary convergence of double sequences of sets and investigate the relationship between them

Asymptotically J_σ-equivalence of sequences of sets

In this study, we introduce the concepts of Wijsman asymptotically J-invariant equivalence (W^L_{J_σ}), Wijsman asymptotically strongly p-invariant equivalence ([W^L_{V_σ}]_p) and Wijsman asymptotically J^*-invariant equivalence (W^L_{J^*_σ}). Also, we investigate the relationships among the concepts of Wijsman asymptotically invariant equivalence, Wijsman asymptotically invariant statistical equivalence, W^L_{J_σ}, [W^L_{V_σ}]_p and W^L_{J^*_σ

Lacunary statistical convergence of double sequences of sets

In this paper, we study the concepts of Wijsman statistical convergence, Wijsman lacunary statistical convergence, Wijsman lacunary convergence and Wijsman strongly lacunary convergence double sequences of sets and investigate the relationship among them

On strongly lacunary summability of sequences of sets

In this paper, we introduce the concept of Wijsman strongly lacunary summability for set sequences. Then, we discus its relation with Wijsman strongly Ces`aro summability. Furthermore, we also give its relation with Wijsman almost convergenc