Invariant convergence in asymmetric metric spaces

In the first chapter, the historical development of the subject discussed. In the se\-cond chapter, some basic concepts are given that will be used in other sections. In the third chapter, asymmetric metric spaces have been analyzed in detail. In the fourth chapter, the concepts of invariant convergence, statistical invariant convergence, invariant Cauchy sequence, invariant statistical Cauchy sequence have been defined in asymmetric metric spaces and the relations between the concepts have been given. In addition, some theorems and results have been obtained by defining the concepts of invariant continuity and invariant compactness in asymmetric metric spaces. In the fifth chapter, the concepts of strong lacunary invariant convergence and lacunary invariant statistical convergence in asymmetric metric spaces are defined and the relations between the concepts are examined. In the sixth chapter, the concepts of $\mathcal{I}_\sigma$-convergence, $\mathcal{I}^*_\sigma$-convergence, $\mathcal{I}_\sigma$-Cauchy and $\mathcal{I}_\sigma$-compactness in asymmetric metric spaces have been defined and some results have been given.