Some types of i̇deal convergence in locally solid Riesz spaces

This thesis consists of five chapters. In the first chapter, the local solid Riesz spaces are briefly mentioned and in the second chapter, the related literature is investigated. In the third chapter, some basic concepts and definitions are given. The fourth chapter, where the original results of the thesis are given, is divided into three part. In the first part of fourth chapter, it has been shown that the notion of ideal in summability theory and the ideal which is defined by the Boolean ring in algebra are equivalent concepts. In the second part of fourth chapter, the concept of weighted lacunary statistical convergence in locally solid Riesz space is defined, some inclusion relations are given and some topological properties of the related space are investigated. In the third part of the fourth chapter, the notions of statistical convergence and lacunary statistical convergence of double sequences defined by weight function in a locally solid Riesz space are introduced and some inclusion relations are investigated. In the last chapter, the results obtained are evaluated.