Lacunary I_σ-convergence

Abstract

In this study, the concept of lacunary invariant uniform density of any subset A of the set N of positive integers is defined. Associate with this, the concept of lacunary I-invariant convergence for real number sequences is given. Also, we examine relationships between this new type convergence concept and the concepts of lacunary invariant summability, strongly lacunary q-invariant convergence and lacunary invariant statistical convergence which are studied in this area before. Finally, introducing lacunary I^*-invariant convergence concept and lacunary I-invariant Cauchy sequence concepts, we give the relationships among these concepts and relationships with lacunary I-invariant convergence concept