On lacunary ideal convergence types

This thesis study consists of five chapters. In the first chapter, the historical development of the subject addressed in this study is examined. In the second chapter, some fundamental concepts required for a clearer understanding of the study are presented. In the third chapter, the notions of la cunary-convergence, lacunary-convergence and lacunary-Cauchy sequence, lacunary-Cauchy sequence, together with strong lacunary-convergence, strong lacunary-convergence and strong lacunary-Cauchy sequence, strong lacunary-Cauchy sequence, are introduced; their specific properties and the relationships between these notions are explained by means of theorems. In the fourth chap ter, the notions of lacunary 2-convergence, lacunary 2-convergence and lacunary 2-Cauchy sequence, lacunary 2-Cauchy sequence, together with strong lacunary 2-convergence, strong lacunary 2-convergence and strong lacunary 2-Cauchy se quence, strong lacunary 2-Cauchy sequence, are introduced; their specific prop erties and the relationships between them are again established by means of the orems. In the fifth and final chapter, the references from the literature that were used throughout the study are listed.