In this work, we introduce a new 2-norm generated by bounded linear functionals on a normed space... more In this work, we introduce a new 2-norm generated by bounded linear functionals on a normed space X with dimension dim(X) ? 2, and investigate its relationship with the G?hler?s 2-norm [Lineare 2-normierte R?ume, Math. Nachr.]. We also derive a norm on X to explore its relation with the usual norm on X.
Contemporary analysis and applied mathematics, Aug 21, 2015
We revisit the space ℓ p of p-summable sequences of real numbers. In particular, we show that thi... more We revisit the space ℓ p of p-summable sequences of real numbers. In particular, we show that this space is actually contained in a (weighted) inner product space. The relationship between ℓ p and the (weighted) inner product space that contains ℓ p is studied. For p > 2, we also obtain a result which describe how the weighted inner product space is associated to the weights.
The aim of this paper is to introduce a new concept for strong almost Pringsheim convergence with... more The aim of this paper is to introduce a new concept for strong almost Pringsheim convergence with respect to an Orlicz function, combining with Riesz mean for double sequences and a double lacunary sequence. In addition, we study almost weighted lacunary statistical convergence for double sequences and present some inclusion theorems.
ABSTRACT The aim of this paper is to introduce some new sequence spaces of lacunary convergent se... more ABSTRACT The aim of this paper is to introduce some new sequence spaces of lacunary convergent sequences combining with Riesz mean and generalized difference matrix by using an Orlicz function. Further, we define a new concept, named Bm -weighted lacunary statistical convergence and examine some connections between this notion with the concept of Bm -lacunary statistical convergence and Bm -weighted statistical convergence. Also, some topological properties of these new sequence spaces are investigated.
There are two known 2-norms defined on the space of p-summable sequences of real numbers. The fir... more There are two known 2-norms defined on the space of p-summable sequences of real numbers. The first 2-norm is a special case of Gähler’s formula [Mathematische Nachrichten, 1964], while the second is due to Gunawan [Bulletin of the Australian Mathematical Society, 2001]. The aim of this paper is to define a new 2-norm on `p and prove the equivalence among these three 2-norms.
Game theory is a mathematical approach to analyze the state of competition between players. The f... more Game theory is a mathematical approach to analyze the state of competition between players. The foundations of this theory go back about 170 years, and the main development of the subject is based on the last 55 years. In this study, the effect of game theory on political elections and political behaviors has been examined. The Nash equilibrium is investigated by creating a mathematical model of the gains and losses that two political parties obtain in the elections according to the coalition formation status of two political parties by using the Prisoners' Dilemma game model in cooperative and non cooperative games.
In this work, we obtain a generalization of asymptotically deferred statistical equivalence of no... more In this work, we obtain a generalization of asymptotically deferred statistical equivalence of non-negative real-valued sequences with the aid of a modulus function. Further, we examine some of main properties of asymptotically deferred f-statistical equivalence and obtain some equivalence results and inclusion relations.
Recently, Konca et al. (2015a) have revisited the space p of p -summable sequences of real number... more Recently, Konca et al. (2015a) have revisited the space p of p -summable sequences of real numbers and have shown that this space is actually contained in a weighted inner product space called 2 v . In another paper, Konca et al. (2015b) have investigated the space p to show that it is also contained in a weighted 2-inner product space. In this work, we show in the details that p is dense in 2 v as a normed space, and as a 2-normed space. Further, we prove that 2 v is separable and conclude that it is isometric to the completion of p .
Motivated by the Arhangel’skii “s-Lindelöf cardinal function” definition, Kočinac and Konca defin... more Motivated by the Arhangel’skii “s-Lindelöf cardinal function” definition, Kočinac and Konca defined and studied set covering properties and set star covering properties. In this paper, we present results on the star covering properties called set star-Menger and set strongly star-Menger. We investigate the relationship among set star-Menger, set strongly star-Menger and other related properties and study the topological properties of set star-Menger and set strongly star-Menger properties.
06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun... more 06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Bu tez çalışması beş bölümden oluşmaktadır. Birinci bölümde, bazı temel tanım ve teoremler verildi. İkinci bölümde, 2-norm ve n-norm kavramları ile ilgili bazı temel tanım ve teoremler verildi. İkinci bölümün bir kısmı, üçüncü bölüm ve dördüncü bölümler bu tezin orijinal kısmını oluşturmaktadır. Üçüncü bölümde 2-normlu uzaylarla ilgili kısımlar bulunurken üçüncü bölümde n-normlu uzaylarla ilgili çalışmalar yer almaktadır. Üçüncü bölümde, iki alt başlık yer almaktadır. Bu bölümün ilk kısmında, yeni bir genelleştirilmiş fark matrisi tanımlanarak 2-normlu uzayda bazı -fark istatistiksel yakınsak dizi uzayları tanıtıldı ve bazı topolojik özellikleri incelendi...
In this paper, we define and study the concept of double weighted lacunary almost statistical con... more In this paper, we define and study the concept of double weighted lacunary almost statistical convergence of order α. Further, some inclusion relations have been examined. Mathematics Subject Classification (2010): 40B05; 40C05; 40A35; 40G15; 46A45
In this work, we introduce the concepts of $\mathcal{I}$-statistical convergence and $\mathcal{I}... more In this work, we introduce the concepts of $\mathcal{I}$-statistical convergence and $\mathcal{I}$-lacunary statistical convergence of double sequences defined by weight functions in a locally solid Riesz space based on the notion of the ideal of subsets of $\mathbb{N}\times\mathbb{N}$. We also examine some inclusion relations of these concepts.
Bu makalede, S ( ) R, θ ( ) I veya agirlikli lacunary I-istatistiksel yakinsaklik ile [ ] R p r θ... more Bu makalede, S ( ) R, θ ( ) I veya agirlikli lacunary I-istatistiksel yakinsaklik ile [ ] R p r θ I -toplanabilirlik kavramlari tanimlanmistir ve bazi kapsama bagintilari arastirilmistir.
In the present paper, we introduce some new sequence spaces derived by Riesz mean and the notions... more In the present paper, we introduce some new sequence spaces derived by Riesz mean and the notions of almost and strongly almost convergence in a real 2normed space. Some topological properties of these spaces are investigated. Further, new concepts of statistical convergence which will be called weighted almost statistical convergence, almost statistical convergence and , n Rp statistical convergence in a real 2normed space, are defined. Also, some relations between these concepts are investigated.
As in 2-normed spaces, we can also give two definitions for Cauchy sequences in n-normed spaces. ... more As in 2-normed spaces, we can also give two definitions for Cauchy sequences in n-normed spaces. It is known that in some cases, especially in the finite dimensional case and the standard case, two definitions are equivalent. What is not clear is in the infinite dimensional case. In this paper, we will prove that these two definitions are still equivalent in `p space.
FOURTH INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2020), 2021
In this paper we introduce some new types of star covering properties which we call set (strongly... more In this paper we introduce some new types of star covering properties which we call set (strongly) star Menger, set (strongly) star Rothberger, set (strongly) star Hurewicz properties. We consider also weaker versions of these properties, discuss their relationships with some other selective covering properties, and study topological properties of introduced classes of spaces.
In this work, we introduce a new 2-norm generated by bounded linear functionals on a normed space... more In this work, we introduce a new 2-norm generated by bounded linear functionals on a normed space X with dimension dim(X) ? 2, and investigate its relationship with the G?hler?s 2-norm [Lineare 2-normierte R?ume, Math. Nachr.]. We also derive a norm on X to explore its relation with the usual norm on X.
Contemporary analysis and applied mathematics, Aug 21, 2015
We revisit the space ℓ p of p-summable sequences of real numbers. In particular, we show that thi... more We revisit the space ℓ p of p-summable sequences of real numbers. In particular, we show that this space is actually contained in a (weighted) inner product space. The relationship between ℓ p and the (weighted) inner product space that contains ℓ p is studied. For p > 2, we also obtain a result which describe how the weighted inner product space is associated to the weights.
The aim of this paper is to introduce a new concept for strong almost Pringsheim convergence with... more The aim of this paper is to introduce a new concept for strong almost Pringsheim convergence with respect to an Orlicz function, combining with Riesz mean for double sequences and a double lacunary sequence. In addition, we study almost weighted lacunary statistical convergence for double sequences and present some inclusion theorems.
ABSTRACT The aim of this paper is to introduce some new sequence spaces of lacunary convergent se... more ABSTRACT The aim of this paper is to introduce some new sequence spaces of lacunary convergent sequences combining with Riesz mean and generalized difference matrix by using an Orlicz function. Further, we define a new concept, named Bm -weighted lacunary statistical convergence and examine some connections between this notion with the concept of Bm -lacunary statistical convergence and Bm -weighted statistical convergence. Also, some topological properties of these new sequence spaces are investigated.
There are two known 2-norms defined on the space of p-summable sequences of real numbers. The fir... more There are two known 2-norms defined on the space of p-summable sequences of real numbers. The first 2-norm is a special case of Gähler’s formula [Mathematische Nachrichten, 1964], while the second is due to Gunawan [Bulletin of the Australian Mathematical Society, 2001]. The aim of this paper is to define a new 2-norm on `p and prove the equivalence among these three 2-norms.
Game theory is a mathematical approach to analyze the state of competition between players. The f... more Game theory is a mathematical approach to analyze the state of competition between players. The foundations of this theory go back about 170 years, and the main development of the subject is based on the last 55 years. In this study, the effect of game theory on political elections and political behaviors has been examined. The Nash equilibrium is investigated by creating a mathematical model of the gains and losses that two political parties obtain in the elections according to the coalition formation status of two political parties by using the Prisoners' Dilemma game model in cooperative and non cooperative games.
In this work, we obtain a generalization of asymptotically deferred statistical equivalence of no... more In this work, we obtain a generalization of asymptotically deferred statistical equivalence of non-negative real-valued sequences with the aid of a modulus function. Further, we examine some of main properties of asymptotically deferred f-statistical equivalence and obtain some equivalence results and inclusion relations.
Recently, Konca et al. (2015a) have revisited the space p of p -summable sequences of real number... more Recently, Konca et al. (2015a) have revisited the space p of p -summable sequences of real numbers and have shown that this space is actually contained in a weighted inner product space called 2 v . In another paper, Konca et al. (2015b) have investigated the space p to show that it is also contained in a weighted 2-inner product space. In this work, we show in the details that p is dense in 2 v as a normed space, and as a 2-normed space. Further, we prove that 2 v is separable and conclude that it is isometric to the completion of p .
Motivated by the Arhangel’skii “s-Lindelöf cardinal function” definition, Kočinac and Konca defin... more Motivated by the Arhangel’skii “s-Lindelöf cardinal function” definition, Kočinac and Konca defined and studied set covering properties and set star covering properties. In this paper, we present results on the star covering properties called set star-Menger and set strongly star-Menger. We investigate the relationship among set star-Menger, set strongly star-Menger and other related properties and study the topological properties of set star-Menger and set strongly star-Menger properties.
06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun... more 06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Bu tez çalışması beş bölümden oluşmaktadır. Birinci bölümde, bazı temel tanım ve teoremler verildi. İkinci bölümde, 2-norm ve n-norm kavramları ile ilgili bazı temel tanım ve teoremler verildi. İkinci bölümün bir kısmı, üçüncü bölüm ve dördüncü bölümler bu tezin orijinal kısmını oluşturmaktadır. Üçüncü bölümde 2-normlu uzaylarla ilgili kısımlar bulunurken üçüncü bölümde n-normlu uzaylarla ilgili çalışmalar yer almaktadır. Üçüncü bölümde, iki alt başlık yer almaktadır. Bu bölümün ilk kısmında, yeni bir genelleştirilmiş fark matrisi tanımlanarak 2-normlu uzayda bazı -fark istatistiksel yakınsak dizi uzayları tanıtıldı ve bazı topolojik özellikleri incelendi...
In this paper, we define and study the concept of double weighted lacunary almost statistical con... more In this paper, we define and study the concept of double weighted lacunary almost statistical convergence of order α. Further, some inclusion relations have been examined. Mathematics Subject Classification (2010): 40B05; 40C05; 40A35; 40G15; 46A45
In this work, we introduce the concepts of $\mathcal{I}$-statistical convergence and $\mathcal{I}... more In this work, we introduce the concepts of $\mathcal{I}$-statistical convergence and $\mathcal{I}$-lacunary statistical convergence of double sequences defined by weight functions in a locally solid Riesz space based on the notion of the ideal of subsets of $\mathbb{N}\times\mathbb{N}$. We also examine some inclusion relations of these concepts.
Bu makalede, S ( ) R, θ ( ) I veya agirlikli lacunary I-istatistiksel yakinsaklik ile [ ] R p r θ... more Bu makalede, S ( ) R, θ ( ) I veya agirlikli lacunary I-istatistiksel yakinsaklik ile [ ] R p r θ I -toplanabilirlik kavramlari tanimlanmistir ve bazi kapsama bagintilari arastirilmistir.
In the present paper, we introduce some new sequence spaces derived by Riesz mean and the notions... more In the present paper, we introduce some new sequence spaces derived by Riesz mean and the notions of almost and strongly almost convergence in a real 2normed space. Some topological properties of these spaces are investigated. Further, new concepts of statistical convergence which will be called weighted almost statistical convergence, almost statistical convergence and , n Rp statistical convergence in a real 2normed space, are defined. Also, some relations between these concepts are investigated.
As in 2-normed spaces, we can also give two definitions for Cauchy sequences in n-normed spaces. ... more As in 2-normed spaces, we can also give two definitions for Cauchy sequences in n-normed spaces. It is known that in some cases, especially in the finite dimensional case and the standard case, two definitions are equivalent. What is not clear is in the infinite dimensional case. In this paper, we will prove that these two definitions are still equivalent in `p space.
FOURTH INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2020), 2021
In this paper we introduce some new types of star covering properties which we call set (strongly... more In this paper we introduce some new types of star covering properties which we call set (strongly) star Menger, set (strongly) star Rothberger, set (strongly) star Hurewicz properties. We consider also weaker versions of these properties, discuss their relationships with some other selective covering properties, and study topological properties of introduced classes of spaces.
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