INTUITIONISTIC FUZZY I-CONVERGENT DIFFERENCE SEQUENCE SPACES DEFINED BY COMPACT OPERATOR

In this paper, we introduce and study the intuitionistic fuzzy $I$-convergent difference sequence spaces  ${I}^{(\mu,\upsilon)}(T,\Delta)$ and  ${I^{0}}^{(\mu,\upsilon)}(T,\Delta)$ using by compact operator. Also we introducce a new concept, called closed ball in these spaces. By the helping of these notions, we establish a new topological space and investigate some topological properties in intuitionistic fuzzy $I$-convergent difference sequence spaces  ${I}^{(\mu,\upsilon)}(T,\Delta)$ and  ${I^{0}}^{(\mu,\upsilon)}(T,\Delta)$ using by compact operator

ON GENERALIZED STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES VIA IDEALS IN INTUITIONISTIC FUZZY NORMED SPACES

In this paper, we introduce the concept of I₂-lacunary statistical convergence and strongly I₂-lacunary convergence with respect to the intuitionistic fuzzy norm (μ,v), investigate their relationship, and make some observations about these classes. We mainly examine the relation between these two new methods and the relation between I₂-statistical convergence in the corresponding intuitionistic fuzzy normed space

Some Topological Properties of Intuitionistic Fuzzy Normed Spaces

In 1986, Atanassov introduced the concept of intuitionistic fuzzy set theory which is based on the extensions of definitions of fuzzy set theory given by Zadeh. This theory provides a variable model to elaborate uncertainty and vagueness involved in decision making problems. In this chapter, we concentrate our study on the ideal convergence of sequence spaces with respect to intuitionistic fuzzy norm and discussed their topological and algebraic properties

New notions on ideal convergence of triple sequences in neutrosophic normed spaces

The usual convergence of sequences has many generalizations with the aim of providing deeper insights into the summability theory. In this paper, following a very recent and new approach, we introduce the notion of I3 and I*3−convergence of triple sequences in neutrosophic normed spaces mainly as a generalization of statistical convergence of triple sequences. We investigate a few fundamental properties and study the relationship between the two notions. We also introduce and investigate the concept of I3 and I*3−Cauchy sequence of triple sequences and show that the condition (AP3) plays a crucial role to study the interrelationship between them.Publisher's Versio

On Wijsman Strongly I2 - Lacunary Convergence of Double Sequences in Neutrosophic Metric Spaces

The concept of Wijsman I2- Statistical Convergence (WI2StC), Wi[1]jsman I2 - Lacunary Statistical Convergence (WI2LStC), Wijsman Strongly I2 - Lacunary Convergence (WSI2LC) and Wijsman Strongly I2 - Cesaro Convergence (WSI2CeC) of double sequences in the Neutrosophic Metric Spaces (NMS) are examined in this paper. Ad[1]ditionally, we introduce the concepts of Wijsman Strongly I ∗ 2 - La[1]cunary Convergence (WSI∗ 2LC), Wijsman Strongly I2- Lacunary Cauchy (WSI2LCa), and Wijsman Strongly I ∗ 2 - Lacunary Cauchy (WSI∗ 2LCa) sequence in NMS and establish impressive results

On quasi statistical convergence in gradual normed linear spaces

During the last few years, enormous works by different researchers have been carried out in summability theory by linking different notions of convergence of sequences. In the present paper, we introduce the concept of quasi statistical convergence and strong quasi statistical summability in gradual normed linear spaces. We investigate some of its basic properties and the interrelationship between the newly introduced notions. It has been observed that every gradual quasi statistical convergent sequence is gradual quasi statistical bounded but not necessarily gradual bounded. Finally, we introduce the concept of gradual quasi statistical Cauchy sequences and show that every gradual quasi statistical convergent sequence is a gradual quasi statistical Cauchy sequence.Publisher's Versio