Invariant convergence types in fuzzy normed spaces

This thesis study consists of six chapters. In the first chapter, the types of convergence discussed in the study and the historical development of the studied space are mentioned. In the second part, some concepts that form the basis of the study are given. In the third chapter, invariant convergence and invariant Cauchy sequence in fuzzy normed spaces are defined and related theorems are given with their proofs. In the fourth chapter, lacunary invariant convergence and strong lacunary invariant convergence with respect to fuzzy norm are given and some important properties are examined. In the fifth chapter, the concepts of invariant statistical convergence and statistical invariant convergence according to fuzzy norm are introduced and some of their properties are given and the relationship between these two convergence types is examined. In addition, the relationship between invariant statistical convergence and invariant convergence has been proven and the invariant statistical Cauchy sequence is given. Finally, in the sixth chapter, the articles and books used throughout the thesis are listed as references.