Yazar "İlkhan, Merve" seçeneğine göre listele

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    A New Modular Space Derived by Euler Totient Function
    (Murat TOSUN, 2019) İlkhan, Merve; Kara, Emrah Evren; Usta, Fuat
    In this study, we introduce the Euler Totient sequence spaces  in generalized Orlicz space and  we examine some topological properties of these spaces by using the Luxemburg norm.
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    A study on Matrix Domain of Riesz-Euler Totient Matrix in the Space of $p$-Absolutely Summable Sequences
    (Emrah Evren KARA, 2021) İlkhan, Merve; Bayrakdar, Mehmet Akif
    In this study, a special lower triangular matrix derived by combining Riesz matrix and Euler totient matrix is used to construct new Banach spaces. $\alpha-$,$\beta-$,$\gamma-$duals of the resulting spaces are obtained and some matrix operators are characterized. Finally by the aid of measure of non-compactness, the conditions for which a matrix operator on these spaces is compact are determined.
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    Bazı fark dizi uzayları üzerinde matris dönüşümleri
    (Düzce Üniversitesi, 2014) İlkhan, Merve; Kara, Emrah Evren
    Bu tez çalışmasında yeni bir fark matrisi olan T=(t_nk ) matrisi, her n?N için t_n>0 ve (t_n )?c\c_0 olmak üzere her n,k?N için t_nk={?(t_n&,&k=n@-1/t_n &,&k=n-1@0&,&0?kn)? şeklinde tanımlanmıştır. Daha sonra T matrisi kullanılarak 1?p?? için l_p (T),c_0 (T) ve c(T) dizi uzayları oluşturulmuştur. Bu uzaylar ile ilgili bazı teoremler ve kapsama bağıntıları verilmiştir. Ayrıca bu uzayların ?-,?-,?- dualleri belirlenmiş ve Schauder bazları bulunmuştur. Son olarak bu uzaylar ile bazı klasik dizi uzayları arasındaki matris dönüşümlerinin sınıfları karakterize edilmiştir.
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    Bazı metrik uzaylar üzerinde Bourbaki-sınırlılık ve Bourbaki-tamlık
    (Düzce Üniversitesi, 2018) İlkhan, Merve; Kara, Emrah Evren
    Bu tez çalışmasında asimetrik metrik uzaylarda Bourbaki sınırlılık ve dış Bourbaki sınırlılık kavramları tanımlandı ve bu kavramlar üzerine çalışıldı. Asimetrik metrik uzaylarda Bourbaki Cauchy ve kofinal Bourbaki Cauchy dizileri tanımlandıktan sonra Bourbaki sınırlılığın bu diziler yardımıyla karakterize edilip edilemeyeceği araştırıldı. Ayrıca bu diziler kullanılarak asimetrik metrik uzaylarda farklı tipte tamlık tanımları verildi. Asimetrik metrik uzaylarda kompaktlık, dizisel kompaktlık ve düzgün yerel kompaktlık ile ilgili önemli bazı sonuçlar elde edildi. Asimetrik metrik uzaylarda doğal yoğunluk kavramı kullanılarak yakınsaklık, Cauchy dizileri, limit noktası ve yığılma noktası gibi temel kavramlar genelleştirildi ve bazı ana sonuçlar elde edildi. Metrik uzaylardaki durumun aksine bu kavramlar ile ilgili bazı farklılıkların olduğu gözlemlendi. Tezin son bölümünde metrik uzaylarda istatistiksel Bourbaki Cauchy dizisi olarak adlandırılan dizilerin yeni bir sınıfı tanımlanarak Bourbaki tamlığa denk yeni bir şart ifade edildi. İstatistiksel Bourbaki Cauchy dizilerini koruyan istatistiksel Bourbaki Cauchy regüler fonksiyonu tanımladıktan sonra bu fonksiyonlar yardımıyla Bourbaki tamlık ve Bourbaki sınırlılığın bazı yeni karakterizasyonları sunuldu.
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    BOURBAKI COMPLETENESS IN QUASI METRIC SPACES
    (Mathematical Research Press-Math Res, 2019) İlkhan, Merve; Kara, Emrah Evren
    The main purpose of this paper is to define a new type of boundedness in a quasi metric space. We introduce some new notions of completeness by clustering sequences belonging to the classes larger than the classes of Cauchy sequences in some sense. We also obtain some interesting results related to the compactness.
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    Certain Geometric Properties and Matrix Transformations on a Newly Introduced Banach Space
    (2020) İlkhan, Merve
    The main purpose of this study is to characterize some matrix classes from classical sequencespaces into a newly introduced space and find the norm of some special matrix operators.Also, we give certain geometric properties of this space.
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    Compact Operators on Generalized Fibonacci Spaces
    (Amer Inst Physics, 2019) İlkhan, Merve; Usta, Fuat; Kara, Emrah Evren
    The main purpose of this paper is to characterize compactness of certain matrix operators on the generalized Fibonacci space by using the Hausdorff measure of non-compactness.
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    Domain of Jordan Totient Matrix in the Space of Almost Convergent Sequences
    (2022) İlkhan, Merve; Güneş, Gizemnur
    In this paper, the notion of almost convergence is used to obtain a space as the domain of a regular matrix. After defining a new type of core for complex-valued sequences, certain inclusion theorems are proved.
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    Multiplication operators on Cesàro second order function spaces
    (Birkhauser Verlag AG, 2019) İlkhan, Merve; Demiriz, Serkan; Kara, Emrah Evren
    In this article, we investigate bounded, invertible and compact multiplication operators on the second order Cesàro function spaces. © 2019, Springer Nature Switzerland AG.
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    A NEW BANACH SPACE DEFINED BY EULER TOTIENT MATRIX OPERATOR
    (Element, 2019) İlkhan, Merve; Kara, Emrah Evren
    The main object of this paper is to introduce a new Banach space derived by using a matrix operator which is comprised of Euler's totient function. Also, we determine alpha, beta, gamma-duals of this space and characterize some matrix classes on this new space. Finally, we obtain necessary and sufficient conditions for some matrix operators to be compact.
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    A New Class Of s-TYPE ( , , ( )) Operators
    (2019) Alp, Pınar Zengin; İlkhan, Merve
    In this paper, we define a new class of s-type ( , , ( )) operators, , ,, , Also we showthat this class is a quasi-Banach operator ideal and we study on the properties of the classeswhich are produced via different types of s-numbers.
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    A New Paranormed Sequence Space Defined by Euler Totient Matrix
    (2019) İlkhan, Merve; Demiriz, Serkan; Kara, Emrah Evren
    In the present paper, by using the regular matrix given by Euler Totient function, we give a new paranormed sequence space ,(?,p) and prove that the spaces ,(?,p) and ,(p) are linearly isomorphic. Also, we compute ?-,?-,?-duals and the Schauder basis of this space.
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    A new type of statistical Cauchy sequence and its relation to Bourbaki completeness
    (Taylor & Francis As, 2018) İlkhan, Merve; Kara, Emrah Evren
    Bourbaki complete metric spaces are important since they are a class between compact metric spaces and complete metric spaces. The aim of the present paper is to introduce the statistical Bourbaki-Cauchy sequence as a new concept and to give an equivalent condition for a metric space to be Bourbaki complete. Also, Bourbaki complete and Bourbaki-bounded metric spaces are characterized in terms of functions which preserve statistical Bourbaki-Cauchy sequences.
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    Norms and lower bounds of some matrix operators on Fibonacci weighted difference sequence space
    (Wiley, 2019) İlkhan, Merve
    Norm of an operator T : X -> Y is the best possible value of U satisfying the inequality parallel to Tx parallel to(Y) <= U parallel to x parallel to(X), and lower bound for T is the value of L satisfying the inequality parallel to Tx parallel to(Y) >= L parallel to x parallel to(X), where parallel to.parallel to(X) and parallel to.parallel to(Y) are the norms on the spaces X and Y, respectively. The main goal of this paper is to compute norms and lower bounds for some matrix operators from the weighted sequence space. l(p)(w) into a new space called as Fibonacci weighted difference sequence space. For this purpose, we firstly introduce the Fibonacci difference matrix (F) over tilde and the space consisting of sequences whose (F) over tilde -transforms are in l(p)((w) over tilde).
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    Numerical solution of Volterra integral equations via Szász-Mirakyan approximation method
    (John Wiley and Sons Ltd, 2020) Usta, Fuat; İlkhan, Merve; Kara, Emrah Evren
    Szász-Mirakyan operators are a powerful tool that can be used to approximate functions on the unbounded interval (Formula presented.). In this contribution, we propose a numerical solution of Volterra integral equations with the help of Szász-Mirakyan operators. In this direction, we provide both numerical scheme and estimation of error bound of solution. Numerical experiments are also presented, highlighting the performance of the new constructions of proposed algorithm in the context of one-dimensional approximation. © 2020 John Wiley & Sons, Ltd.
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    ON NEW TYPES OF SETS VIA gamma-OPEN SETS IN BITOPOLOGICAL SPACES
    (Ankara Univ, Fac Sci, 2018) İlkhan, Merve; Akyiğit, Mahmut; Kara, Emrah Evren
    In this paper, the concept of (i,j)-gamma-P-open sets in bitopological spaces are introduced and characterizations of their related notions are given.
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    On statistical convergence in quasi-metric spaces
    (Sciendo, 2019) İlkhan, Merve; Kara, Emrah Evren
    A quasi-metric is a distance function which satisfies the triangle inequality but is not symmetric in general. Quasi-metrics are a subject of comprehensive investigation both in pure and applied mathematics in areas such as in functional analysis, topology and computer science. The main purpose of this paper is to extend the convergence and Cauchy conditions in a quasi-metric space by using the notion of asymptotic density. Furthermore, some results obtained are related to completeness, compactness and precompactness in this setting using statistically Cauchy sequences.
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    On The Difference Sequence Space $l_p(\hat{T}^q)$
    (Murat TOSUN, 2019) İlkhan, Merve; Alp, Pınar Zengin
    In this study, we introduce a new matrix $\hat{T}^q=(\hat{t}^q_{nk})$ by\[\hat{t}^q_{nk}=\left \{\begin{array}[c]{ccl}%\frac{q_n}{Q_n} t_n & , & k=n\\\frac{q_k}{Q_n}t_k-\frac{q_{k+1}}{Q_n} \frac{1}{t_{k+1}} & , & k<n\\0 & , & k>n .\end{array}\right.\] where $t_k>0$ for all $n\in\mathbb{N}$ and $(t_n)\in c\backslash c_0$. By using the matrix $\hat{T}^q$, we introduce the sequence space $\ell_p(\hat{T}^q)$ for $1\leq p\leq\infty$. In addition, we give some theorems on inclusion relations associated with $\ell_p(\hat{T}^q)$ and find the $\alpha$-, $\beta$-, $\gamma$- duals of this space. Lastly, we analyze the necessary and sufficient conditions for an infinite matrix to be in the classes $(\ell_p(\hat{T}^q),\lambda)$ or $(\lambda,\ell_p(\hat{T}^q))$, where $\lambda\in\{\ell_1,c_0,c,\ell_\infty\}$.
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    On the Difference Sequence Space `p(Tˆq)
    (2019) Alp, Pınar Zengın; İlkhan, Merve
    In this study, we introduce a new matrix Tˆq = (tˆqnk) bytˆqnk =???qnQntn , k = nqkQntk ?qk+1Qn1tk+1, k < n0 , k > n.where tk > 0 for all n ? N and (tn) ? c\c0. By using the matrix Tˆq, we introduce the sequence space`p(Tˆq) for 1 ? p ? ?. In addition, we give some theorems on inclusion relations associated with `p(Tˆq)and find the ?-, ?-, ?- duals of this space. Lastly, we analyze the necessary and sufficient conditions foran infinite matrix to be in the classes (`p(Tˆq), ?) or (?, `p(Tˆq)), where ? ? {`1, c0, c, `?}.
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    On The Spaces of Linear Operators Acting Between Asymmetric Cone Normed Spaces
    (Springer Basel Ag, 2018) İlkhan, Merve; Alp, Pınar Zengin; Kara, Emrah Evren
    An asymmetric norm is a positive sublinear functional p on a real vector space X satisfying whenever . Since the space of all lower semi-continuous linear functionals of an asymmetric normed space is not a linear space, the theory is different in the asymmetric case. The main purpose of this study is to define bounded and continuous linear operators acting between asymmetric cone normed spaces. After examining the differences with symmetric case, we give some results related to Baire's characterization of completeness in asymmetric cone normed spaces.