Remarkable Applications of Measure of Non-compactness For Infinite System of Differential Equations

The essential goal of our study is to search for a solution of an infinite system of differential equations in two different Banach spaces under certain assumptions by the aid of measure of noncompactness. Also, we establish some interesting examples related to our results

QUASI STATISTICAL CONVERGENCE IN CONE METRIC SPACES

The main purpose of this paper is to define a new type of statisticalconvergence of sequences in a cone metric space and investigate the relationsof these sequences with some other sequences

Matrix transformations on some difference sequence spaces

YÖK Tez No: 379776Bu 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.In this study, a new band matrix T=(t_nk ) was defined as t_nk={?(t_n&,&k=n@-1/t_n &,&k=n-1@0&,&0?kn)? for all n,k?N, where t_n>0 for all n?N and (t_n )?c\c_0. Later, by using the matrix T, the sequence spaces l_p (T),c_0 (T) and c(T) were constructed for 1?p??. Some theorems and inclusion relations related to these spaces were given. Also, ?-,?-,?- duals of these spaces were determined and their Schauder basis were found. Finally, classes of matrix mappings between these spaces and some classical sequence spaces were characterized

Matrix Domain of a Regular Matrix Derived by Euler Totient Function in the Spaces c(0) and c

Ilkhan, Merve/0000-0002-0831-1474WOS: 000511328700003The main purpose of this manuscript is to introduce Banach spaces c(0)(Phi) and c(Phi) as the matrix domain of a regular matrix Phi derived by the Euler totient function. These spaces consist of phi-convergent to zero and phi-convergent sequences, respectively. After determining alpha-, beta- and gamma-duals of these spaces, some matrix classes are characterized. Finally, using the Hausdorff measure of noncompactness, the characterization of some classes of compact operators on the space c(0)(Phi) is given

Norms and lower bounds of some matrix operators on Fibonacci weighted difference sequence space

Ilkhan, Merve/0000-0002-0831-1474WOS: 000503431300003Norm of an operator T : X -> Y is the best possible value of U 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)

Bourbaki-boundedness and Bourbaki-completeness on some metric spaces

YÖK Tez No: 509575Bu 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.In this thesis the concepts of Bourbaki boundedness and outside Bourbaki boundedness are defined in asymmetric metric spaces and these concepts are studied. After defining Bourbaki Cauchy and cofinally Bourbaki Cauchy sequences in asymmetric metric spaces, it is investigated whether Bourbaki boundedness can be characterized by means of these sequences. Moreover by using these sequences, definitions of different type of completeness are given. Some important results are obtained related to compactness, sequentially compactness and uniformly locally compactness in asymmetric metric spaces. By using the notion of natural density, some basic concepts such as convergence, Cauchy sequences, limit point and cluster point are generalized and some fundamental results are obtained on asymmetric metric spaces. Unlike the case of metric spaces, some differences are observed related to these concepts. In the last part of the thesis, a new condition equivalent to Bourbaki completeness is stated by defining a new class of sequences named as a statistical Bourbaki-Cauchy sequence in metric spaces. After defining the statistical Bourbaki Cauchy regular function which is a function preserving statistical Bourbaki Cauchy sequences, some new characterizations of Bourbaki completeness and Bourbaki boundedness are introduced by means of these functions

Certain Geometric Properties and Matrix Transformations on a Newly Introduced Banach Space

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

A study on nonsymmetric cone normed spaces

In the realms of theoretical computer science and approximation theory, asymetric normed spaces play an important role. In this paper, by combining asymmetric norm and cone norm, it is defined asymmetric cone normed spaces. Also, it is introduced and studied some topological concepts in asymmetric cone normed spaces.Teorik bilgisayar bilimi ve yaklaşım teorisi alanlarında asimetrik normlu uzaylar önemli bir rol oynamaktadır. Bu çalışmada asimetrik norm ve konik norm birleştirilerek asimetrik konik normlu uzaylar tanımlanmaktadır. Ayrıca asimetrik konik normlu uzaylarda bazı topolojik kavramlar tanıtılmakta ve çalışılmaktadı

A new conservative matrix derived by Catalan numbers and its matrix domain in the spaces c and c(0)

WOS: 000473303600001The main purpose of this paper is to define a new conservative matrix by means of the fascinating sequence of Catalan numbers and study the matrix domain of this newly introduced matrix in the classical sequence spaces c and . Additionally, after determining the Kothe-Toeplitz dual, generalized Kothe-Toeplitz dual and Garling dual, certain matrix transformations and compact operators are characterized on the new Banach spaces