Some new sequence spaces defined by a modulus function and statistical convergence

SUMMARY PhD Thesis SOME NEW SEQUENCE SPACES DEFINED BY A MODULUS FUNCTION AND STATISTICAL CONVERGENCE Ayhan ESI Fırat University Graduate School of Natural and Applied Sciences Department of Mathematics 1995,Page:60 This thesis consists of four chapters. In the first chapter, some fundamental definitions and theorems which will be used in the sequel of the thesis are given. Second, third and fourth chapters are the original parts of this study. In the second chapter, we present some well-known sequence spaces which are defined by a modulus function and define some new sequence spaces which will be denoted by [w0(A,p,f,s)], [w(A,p,f,s)] and lw»(A,p,f,s)3, where A=(ar!|ç) isa matrix having positive entries and f is a modulus function. The various properties of these spaces and space Llp,f,s] obtained in a special case, are investigated. Furthermore, defining the sequence space [w(A,p,fv,s)3, where veN, some inclusion relations are given between the sequence spaces [w(A,p,f"\s)] and [w(A,p,fu,s)], where u.veN. In the third chapter, we reduce the sequence spaces defined in the second chapter- to [w,f]0,[w,f] andlw.f]^ by taking 8 Cesaro matrix A=(önj()=(C,1)J s=0 andp^l for each k and also some results are expressed. in the fourth chapter, S- 1 statistical convergence concept is given, using these aspects, the relations between [w,f 3 -convergent and [wp] -convergent sequence spaces are qiven. KEY WORDS: Sequence space, paranorm.modulus function, statistical convergence