Yazar "Cakan, Celal" seçeneğine göre listele

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    The Cesaro Core of Double Sequences
    (Hindawi Ltd, 2011) Kayaduman, Kuddusi; Cakan, Celal
    We have characterized a new type of core for double sequences, P-C-core, and determined the necessary and sufficient conditions on a four-dimensional matrix A to yield P-C-core{Ax} subset of alpha(P-core{x}) for all l(2)(infinity).
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    Characterization of P-Core and Absolute Equivalence of Double Sequences
    (Springeropen, 2010) Furkan, Hasan; Cakan, Celal
    The P-core of a double sequence has been defined and it is studied by many authors. In this paper, we have determined two permutations pi(1) and pi(2) on the set of natural numbers for which P-coreA(pi 1)(x) = P-coreA(pi 2)(x) for all x is an element of l(infinity)(2).
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    DOUBLE LACUNARY DENSITY AND LACUNARY STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES
    (Akademiai Kiado Rt, 2010) Cakan, Celal; Altay, Bilal; Coskun, Huesamettin
    In this paper, we have defined double lacunary density and investigated the relation between statistical and lacunary statistical convergence of double sequences. Also, we have solved an inequality related to the lacunary statistical limit superior of real bounded double sequences.
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    The extension of the Knopp core theorem to the sequences of fuzzy numbers
    (Elsevier Science Inc, 2014) Talo, Ozer; Cakan, Celal
    The concept of the core of a sequence of fuzzy numbers has been introduced by Aytar et al. in [The core of a sequence of fuzzy numbers, Fuzzy Sets and Systems, 159(24) (2008) 3369-3379]. Quite recently, some matrix transformations on the classical sets of sequences of fuzzy numbers have been characterized by Talo and Basar in [Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations, Comput. Math. Appl. 58 (2009) 717-733]. In this paper, we have proved a core theorem for sequences of fuzzy numbers which is analogous to the famous Knoop Core Theorem for real sequences. To achieve this goal, we have studied some properties of the lim sup and lim inf of sequences of fuzzy numbers. Also, we have characterized a class of positive regular matrices of fuzzy numbers such that these matrices leave the core of any bounded sequence of fuzzy numbers invariant. (C) 2014 Elsevier Inc. All rights reserved.
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    FB-convergence and a generalization of Knopp's core
    (Walter De Gruyter Gmbh, 2010) Cakan, Celal; Kasap, Zeki
    In this paper, based on F-B-convergence, we introduce the F-B-core of sequences of complex numbers and determine a class of matrices A for which the F-B-core(Ax) is a subset of Knopp's core for all bounded sequences x.
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    Generalized statistical convergence and statistical core of double sequences
    (Springer Heidelberg, 2010) Mursaleen, Mohammad; Cakan, Celal; Mohiuddine, Syed Abdul; Savas, Ekrem
    In this paper we extend the notion of lambda-statistical convergence to the (lambda, A mu)statistical convergence for double sequences x = (x (jk) ). We also determine some matrix transformations and establish some core theorems related to our new space of double sequences S (lambda,A mu).
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    On some new paranormed euler sequence spaces and Euler Core
    (Springer Heidelberg, 2010) Demiriz, Serkan; Cakan, Celal
    In this paper, the sequence spaces e (0) (r) (u, p) and e (c) (r) (u, p) of non-absolute type which are the generalization of the Maddox sequence spaces have been introduced and it is proved that the spaces e (0) (r) (u, p) and e (c) (r) (u, p) are linearly isomorphic to spaces c (0)(p) and c(p), respectively. Furthermore, the alpha-, beta- and gamma-duals of the spaces e (0) (r) (u, p) and e (c) (r) (u, p) have been computed and their bases have been constructed and some topological properties of these spaces have been investigated. Besides this, the class of matrices (e (0) (r) (u, p): A mu) has been characterized, where A mu is one of the sequence spaces a (a), c and c (0) and derives the other characterizations for the special cases of A mu. In the last section, Euler Core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core.
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    On the Cesaro convergence of sequences of fuzzy numbers
    (Pergamon-Elsevier Science Ltd, 2012) Talo, Ozer; Cakan, Celal
    In this paper we have determined necessary and sufficient Tauberian conditions under which convergence follows from (C, 1)-convergence of sequences of fuzzy numbers. (C) 2011 Elsevier Ltd. All rights reserved.
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    ?-REGULAR MATRICES AND A ?-CORE THEOREM FOR DOUBLE SEQUENCES
    (Hacettepe Univ, Fac Sci, 2009) Cakan, Celal; Altay, Bilal; Coskun, Huesamettin
    The famous Knopp Core of a single sequence was extended to the P-core of a double sequence by R.F. Patterson. Recently, the MR-core and sigma-core of real bounded double sequences have been introduced and some inequalities analogues to those for Knoop's Core Theorem have been studied. The aim of this paper is to characterize a class of four-dimensional matrices, and so to obtain necessary and sufficient conditions for a new inequality related to the P- and sigma-cores.
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    The riesz convergence and riesz core of double sequences
    (Springeropen, 2012) Alotaibi, Abdullah M.; Cakan, Celal
    In this article, we have introduced the Riesz convergence and Riesz core of double sequences and determined the necessary and sufficient conditions on a four-dimensional matrix A to yield P-R - core{Ax}. P subset of core{x} and P-R - core{Ax} subset of st(2) - core {x} for all x is an element of l(infinity)(2).
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    The Riesz Core of a Sequence
    (Gazi Univ, 2011) Cakan, Celal; Alotaibi, Abdullah M.
    The Riesz sequence space r(c)(q) including the space c has recently been defined in [14] and its some properties have been investigated. In the present paper, we introduce a new type core, K-q-core, of a complex valued sequence and also determine the required conditions for a matrix B for which K-q-core (Bx) subset of K-core (x), K(q)core (Bx) subset of st(A)-core (x) and K-q-core (Bx) subset of K-q-core (x) hold for all x is an element of l(infinity).
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    ROUGH I-CONVERGENCE
    (De Gruyter Open Ltd, 2014) Duendar, Erdinc; Cakan, Celal
    In this work, using the concept of I-convergence and using the concept of rough convergence, we introduced the notion of rough I-convergence and the set of rough I-limit points of a sequence and obtained two rough I-convergence criteria associated with this set. Later, we proved that this set is closed and convex. Finally, we examined the relations between the set of I-cluster points and the set of rough I-limit points of a sequence.
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    SOME INEQUALITIES RELATED TO THE PRINGSHEIM, STATISTICAL AND ?-CORES OF DOUBLE SEQUENCES
    (Hacettepe Univ, Fac Sci, 2013) Cakan, Celal; Altay, Bilal; Coskun, Husamettin
    The statistical convergence of double sequences was presented by Mursaleen-Edely and Tripathy in two ways, [10, 16]. The statistical core of double sequences was introduced by Cakan- Altay, [1]. The sigma-convergence and sigma-core of double sequences were defined by Cakan-Altay-Mursaleen, [5]. In this paper, we will study some new inequalities related to the Pringsheim, statistical and sigma-cores of double sequences. To achieve this goal, we will characterize some classes of four-dimensional matrices.
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    Some new paranormed difference sequence spaces and weighted core
    (Pergamon-Elsevier Science Ltd, 2012) Demiriz, Serkan; Cakan, Celal
    In this study, we define new paranormed sequence spaces by combining a generalized weighted mean and a difference operator. Furthermore, we compute the alpha-,beta- and gamma- duals and obtain bases for these sequence spaces. Besides this, we characterize the matrix transformations from the new paranormed sequence spaces to the spaces c(0)(q), c(q), l(q) and l(infinity)(q). Finally, weighted core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core. (c) 2012 Elsevier Ltd. All rights reserved.
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    Some Topological and Geometrical Properties of a New Difference Sequence Space
    (Hindawi Publishing Corporation, 2011) Demiriz, Serkan; Cakan, Celal
    We introduce the new difference sequence space a(p)(r)(Delta). Further, it is proved that the space a(p)(r)(Delta) is the BK-space including the space bv(p), which is the space of sequences of pbounded variation. We also show that the spaces a(p)(r)(Delta), and l(p) are linearly isomorphic for 1 <= p < infinity. Furthermore, the basis and the alpha-, beta-and gamma-duals of the space a(p)(r)(Delta) are determined. We devote the final section of the paper to examine some geometric properties of the space a(p)(r)(Delta).
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    SOME TOPOLOGICAL AND GEOMETRICAL PROPERTIES OF THE SEQUENCE SPACE er (u, p)
    (Springer, 2012) Demiriz, Serkan; Cakan, Celal
    In this paper, we introduce the sequence space e(r)(u,p) and investigate its some topological and geometrical properties such as basis, alpha-, beta-, gamma- duals and the uniform Opial property.
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    Tauberian Theorems for Statistically (C, 1)-Convergent Sequences of Fuzzy Numbers
    (Univ Nis, Fac Sci Math, 2014) Talo, Ozer; Cakan, Celal
    In this paper, we have determined necessary and sufficient Tauberian conditions under which statistically convergence follows from statistically (C, 1)-convergence of sequences of fuzzy numbers. Our conditions are satisfied if a sequence of fuzzy numbers is statistically slowly oscillating. Also, under additional conditions it is proved that a bounded sequence of fuzzy numbers which is (C, 1)-level-convergent to its statistical limit superior is statistically convergent