Cilt:68 Sayı:02 (2019) http://hdl.handle.net/20.500.12575/75722 2023-12-06T20:05:40Z I-lacunary statistical convergence of weighted g via modulus functions in 2-normed spaces http://hdl.handle.net/20.500.12575/75965 I-lacunary statistical convergence of weighted g via modulus functions in 2-normed spaces Savaş, Ekrem; Yamancı, Ulaş; Gürdal, Mehmet In this paper, we introduce new concepts of I-statistical convergence and I-lacunary statistical convergence using weighted density via modulus functions. Also, we study the relationship between them and obtain some interesting results. 2019-08-01T00:00:00Z Approximation properties of Bernstein-Kantorovich type operators of two variables http://hdl.handle.net/20.500.12575/75964 Approximation properties of Bernstein-Kantorovich type operators of two variables Karahan, Döne; İzgi, Aydın In this study, the generalized Bernstein-Kantorovich type operators are introduced and some approximation properties of these operators are studied in the space of continuous functions of two variables on a compact set . The convergence rate of these operators are obtained by means of the modulus of continuity. The Voronovskaya type theorem is given and some differential properties of these operators are proved. 2019-08-01T00:00:00Z [1,2]-Complementary connected domination number of graphs-III http://hdl.handle.net/20.500.12575/75963 [1,2]-Complementary connected domination number of graphs-III Mahadevan, G.; Renuka, K. A set S⊆V(G) in a graph G is said to be [1,2]-complementary connected dominating set if for every vertex v∈V-S, 1≤|N(v)∩S|≤2 and <V-S> is connected. The minimum cardinality of [1,2]-complementary connected dominating set is called [1,2]-complementary connected domination number and is denoted by γ_{[1,2]cc}(G). In this paper, we investigate 3-regular graphs on twelve vertices for which γ_{[1,2]cc}(G)=χ(G)=3. 2019-08-01T00:00:00Z On a graph of ideals of a commutative ring http://hdl.handle.net/20.500.12575/75962 On a graph of ideals of a commutative ring Khoramdel, Mehdi; Atani, Shahabaddin Ebrahimi; Pishhesari, Saboura Dolati In this paper, we introduce and investigate a new graph of a commutative ring R, denoted by G(R), with all nontrivial ideals of R as vertices, and two distinct vertices I and J are adjacent if and only if ann(I∩J)=ann(I)+ann(J). In this article, the basic properties and possible structures of the graph G(R) are studied and investigated as diameter, girth, clique number, cut vertex and domination number. We characterize all rings R for which G(R) is planar, complete and complete r-partite. We show that, if (R,M) is a local Artinian ring, then G(R) is complete if and only if Soc(R) is simple. Also, it is shown that if R is a ring with G(R) is r-regular, then either G(R) is complete or null graph. Moreover, we show that if R is an Artinian ring, then R is a serial ring if and only if G(R/I) is complete for each ideal I of R. 2019-08-01T00:00:00Z