Logarithmic convergence types

In the first chapter, the importance of the topics examined in the thesis in the field of mathematics and the literature information summarizing the studies conducted on the topics are given. In the second chapter, the basic definitions and concepts available in the mathematical literature and used in the thesis are mentioned. In the third chapter, the concepts of (H,1)-summability, logarithmic statistical convergence and statistical (H,1)-summability and theorems examining the relations between these concepts are given with their proofs. In the fourth chapter, the concepts of lacunary (H,1)-summability, lacunary strong harmonic summability, lacunary statistical (H,1)-summability and lacunary statistical logarithmic convergence and related theorems are given with their proofs. In the fifth chapter, which is the original part of the thesis, the concepts of logarithmic I and I^*-convergence and logarithmic I and I^*-Cauchy sequence are introduced and their properties are given. In the sixth chapter, which is the last chapter, the sources in the literature used during the thesis study are listed.