Some double sequence spaces defined by a Modulus function

In the first chapter of this work which was prepared as three chapter, definitionsof some notions and important theorems which will be used in the following chapterare given.In the second chapter of this work, by introducing the space Lu (f ) of scalarvalued double sequences and the space Lu (X, f ) of vector valued double sequencessome algebraic and topological properties of these spaces are studied. Also the familyof operators which forms a basis on the spaces Lu (X) and Lu (X, f ) are given.In the last chapter of this work, topological duals of the spaces Lu (X), Lu (X, f )and Lu (f ) are found, and by giving perfectness, normality and monotonicitydefinitions for vector valued double sequence spaces, α and β (ν) duals of the spacesLu (X), Lu (X, f ) and Lu (f ) spaces are determined.KEY WORDS: Double sequence space, Modulus function, paranormed space,vector valued double sequence spaceii