In this thesis we studied αβ-statistical convergence. We started with the discussion of statistical convergence. Later, we gave a brief summary of λ-statistical, lacunary statistical and A−statistical convergences. The concept of αβ-statistical convergence which is the main interest of this thesis has been considered in the last chapter of the thesis. In this chapter we also show that αβ-statistical convergence is a non-trivial extension of statistical, λ-statistical and lacunary statistical convergences. Finally, we introduced boundedness of a sequence in the sense of αβ-statistical convergence.

http://i-rep.emu.edu.tr:8080/jspui/bitstream/11129/1642/1/KukulHande.pdf

αβ− Statistical Convergence

Some new spaces of double sequences

Let @l denote any one of the classical spaces @?"~, c, c"0 and @?"p of bounded, convergent, null and absolutely p-summable sequences, respectively, and @l@^ also be the domain of the generalized difference matrix B(r,s) in the sequence space @l, where 1@?p<~. The present paper is devoted to studying on the sequence space @l@^. Furthermore, the @b- and @c-duals of the space @l@^ are determined, and the Schauder bases for the spaces c@^, c@^"0 and @?@^"p are given, and some topological properties of the spaces c@^"0, @?@^"1 and @?@^"p are examined. Finally, the classes (@l@^"1:@l"2) and (@l@^"1:@l@^"2) of infinite matrices are characterized, where @l"1@?{@?"~,c,c"0,@?"p,@?"1} and @l"2@?{@?"~,c,c"0,@?"1}.

Some new sequence spaces derived by the domain of generalized difference matrix

In the present paper, we introduce a new band matrix and define the sequence space where is the k th Fibonacci number for every . We also establish some inclusion relations concerning this space and determine its α-, β-, γ-duals. Further, we characterize some matrix classes on the space and examine some geometric properties of this space. MSC:11B39, 46A45, 46B45, 46B20.

/pdf/some-topological-and-geometrical-properties-of-new-banach-2jjp4ck38a.pdf

Some topological and geometrical properties of new Banach sequence spaces

In this paper, we introduce the concepts of pointwise and uniform statistical convergence of order α for sequences of real-valued functions. Furthermore, we give the concept of an α-statistically Cauchy sequence for sequences of real-valued functions and prove that it is equivalent to pointwise statistical convergence of order α for sequences of real-valued functions. Also, some relations between S α (f )-statistical convergence and strong w β p (f )-summability are given. MSC: 40A05; 40C05; 46A45

/pdf/on-pointwise-and-uniform-statistical-convergence-of-order-a-49ssp1oaad.pdf

On pointwise and uniform statistical convergence of order α for sequences of functions

Summability Theory and its Applications

λ-Statistical convergence of order α

/pdf/on-some-generalized-difference-sequence-spaces-and-related-evctxn54nv.pdf

Rifat Çolak

Papers

Summability Theory and its Applications

λ-Statistical convergence of order α

On some generalized difference sequence spaces and related matrix transformations

Generalized difference sequence spaces and their dual spaces

λ-Difference sequence spaces of fuzzy numbers