On I-lacunary statistical convergence

This thesis consists of six chapters. First chapter has been devoted to introduction, historical development of the topic and general literature are given. In the second chapter, some basic concepts necessary for a better understanding of work are recalled. In the third chapter, the concepts of I-statistical convergence, I-lacunary statistical convergence and strong I-lacunary summability of real number sequences are introduced and their specifi c properties and relations between these concepts are explained by examples and theorems. In the fourth chapter, the concepts of I-statistical convergence, I-{lambda}-statistical convergence and I-[V,lambda]-summability are given in any normed linear space and their specifi c properties and relations between these concepts are explained by examples and theorems. In the fifth chapter, the concepts given in the third section are generalized where 0<{alpha}<=1; the concepts of I-statistical convergence, I-lacunary statistical convergence and strong I-lacunary summability of order {alpha} for real number sequences are introduced, their specifi c properties and relations between these concepts are explained by examples and theorems. In the sixth section, which is the last chapter, the sources in the literature that have been utilized throughout the study are listed.