Sinan Ercan

• Fırat University

In the present paper, the notion of discrete weighted mean method of summability isextended the concept of statistical convergence. We also give the notion of statistical (M,P_{λ})-summability and [M,P_{λ}]_{q}-summability. We introduced some properties of this modes of convergence

The aim of the present work is to introduce the concepts of deferred weak statistical convergence and deferred weak Cesàro summability on normed spaces. We prove some properties with related to these concepts and we also give some new related notions and some inclusion relations with examples.

In the present paper, we introduce the notion of λm-convergence and λm -boundedness. We examine the relationship of these notions between of the ordinary convergence and ordinary boundedness, respectively. We also introduce new sequence spaces and some topological properties of these spaces. Furthermore, we investigate some inclusion relations betw...

In this paper, we introduce lacunary weak statistical convergence of order α and weak Nθα-convergence for 0<α≤1. We prove some properties of these modes of convergence and give some inclusion relations.

The aim of the present work is to introduce notions of statistical convergence, strongly p-Cesàro summability and the statistically Cauchy sequence of order α in paranormed spaces. Some certain topological properties of these new concepts are examined. Furthermore, we introduce the some inclusion relations among them.

In the present paper, we give the concept of weak λ-statistical convergence of order α and weakly [V,λ]-summability of order α. Some relations between of these concepts and also some relations between weak λ-statistical convergence of order α and strong λ-statistical convergence of order α are examined. © 2018 Politechnica University of Bucharest....

In this paper, we introduce the spaces c(lambda(2), Delta) and c(0)(lambda(2), Delta), which are BK-spaces of non-absolute type and we prove that these spaces are linearly isomorphic to the spaces c and c(0), respectively. Moreover, we give some inclusion relations and compute the alpha-, beta- and gamma-duals of these spaces. We also determine the...

In this paper, we give the notion of λm-boundedness and p-absolute convergenceof type λm and using these notions we define new sequence spaces. We examinesome topological and geometric properties of these spaces. We also establish someinclusion relations concerning these spaces and characterize some matrix classes.

In this paper we introduce a paranormed sequence space BVσ(M, p,q,u) defined by a sequence of Orlicz functions. We examine some properties of this space.

In this paper, we compute alpha-, beta- and gamma- duals of the new BK-spaces ℓ∞ (λm), c(λm) and c(λm). We also give some classes of matrix transformations from these spaces to ℓ∞, c, c0, f and f0.

In this paper, we introduce the spaces c(λ², ∆) and c0 (λ², ∆), which are BK-spaces of non-absolute type and we prove that these spaces are linearly isomorphic to the spaces cand c0, respectively. Moreover, we give some inclusion relations and compute the α-, β- and γ- duals of these spaces. We also determine the Schauder basis of the c(λ², ∆) and...

In the present paper, we introduce the sequence space (Formula presented.) using a new regular matrix of Fibonacci numbers, where (Formula presented.). We investigate its topological properties such as Schauder basis, (Formula presented.) and (Formula presented.) duals and its geometric properties like uniformly convex, strictly convex and super-re...

In the present paper, we studied the new properties of BK-spaces which were defined using regular matrix of Fibonacci numbers in [1]. We computed alpha-, beta-, gamma- duals of these spaces and obtained Schauder basis. We also derived some topological properties of these spaces.

We determine the relations between the classes S ^ λ of almost λ -statistically convergent sequences and the relations between the classes V ^ , λ of strongly almost V , λ -summable sequences for various sequences λ , μ in the class Λ . Furthermore we also give the relations between the classes S ^ λ of almost λ -statistically convergent sequences...

In this paper, we introduce the notion of λν-convergent and bounded sequences. Further, we introduce the spaces ℓλ∞ (Δν), cλ0 (Δv) and cλ (Δν), which are BK-spaces of non-absolute type and we prove that these spaces are linearly isomorphic to the spaces ℓ∞, c0 and c, respectively. Moreover, we establish some inclusion relations between these spaces...