$\mathfrak{I}$-Limit and $\mathfrak{I}$-Cluster Points for Functions Defined on Amenable Semigroups

Abstract

In this paper firstly, for functions defined on discrete countable amenable semigroups (DCASG), the notions of I-limit and I-cluster points are introduced. Then, for the functions, the notions of I-limit superior and inferior are examined.

$\mathcal{I}_2$-Uniform Convergence of Double Sequences of Functions In $2$-Normed Spaces

“…Now, we recall the concept of 2-normed space, ideal convergence and some fundamental definitions and notations (See [1,2,3,4,5,6,13,14,15,16,19,21,22,23,24,25,26,27,31,32,36,38]).…”

Strongly Lacunary $\mathcal{I}^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}^{\ast }$-Cauchy Sequence

“…Also, we defined the concept of strongly lacunary I * -Cauchy sequence and investigated the relations between strongly lacunary I-Cauchy sequence and strongly lacunary I * -Cauchy sequence. Now, we recall some basic concepts and definitions (see [3,4,[6][7][8][12][13][14][15][16][17][18][19][20][21]). A family of sets I ⊆ 2 N is called an ideal if and only if…”

On Rough $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence for Functions Defined on Amenable Semigroups

“…Also, Dündar et al [18] defined rough ideal convergence and some properties in ASG. Recently, some authors studied on the new concepts in ASG (see [19][20][21][22]). First of all, we remember the basic definitions and concepts that we will use in our study such as amenable semigroups, rough convergence, rough ideal convergence, etc.…”