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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.

Paranormed spaces are important as a generalization of the normed spaces in terms of having more general properties. The aim of this study is to introduce a new paranormed space vertical bar phi(z)vertical bar (p) over the paranormed space l(p) using Euler totient means, where p = (p(k)) is a bounded sequence of positive real numbers. Besides this, we investigate topological properties and compute the alpha-, beta-, and gamma duals of this paranormed space. Finally, we characterize the classes of infinite matrices (vertical bar phi(z)vertical bar (p) , lambda) and (lambda, vertical bar phi(z)vertical bar (p)), where lambda is any given sequence space. WOS:000546263500004

In this study, we present the numerical solution of Riesz fractional differential equation with the help of meshless method. In accordance with this purpose, we benefit the radial basis functions (RBFs) interpolation method and conformable fractional calculus. We finally present the results of numerical experimentation to show that presented algorithm provide successful consequences.

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.

In theoretical and applied areas of mathematics, one can work with sets endowed with several structures. A bitopological space is a set equipped with two topologies. In this paper, some types of open sets weaker than delta-open sets are generalized to bitopological spaces and their corresponding interior and closure operators are introduced. The relations between these sets and counter examples for the reverse relations are given. By using these sets, new types of continuous functions are defined and some of their properties are studied in bitopological spaces.

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. Bu çalışmada, Euler Totient fonksiyonu ile oluşturulan regüler bir matrisin kullanılmasıyla, yeni bir paranormlu uzay olan ,(?,p) uzayını tanımladık ve bu uzayın ,(p) uzayına lineer izomorf olduğunu gösterdik. Ayrıca bu uzayın ?-,?-,?-duallerini ve Schauder bazını hesapladık.

WOS: 000501549100033 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.

The main objective of this work is to develop fixed point results for (alpha, phi)-Meir-Keeler contractive mappings in generalized rectangular b-metric spaces and to investigate the uniqueness of fixed points. WOS:000577160000001

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.

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, `?}.

In this study, by using the Hausdorff measure of non-compactness, we obtain the necessary and sufficient conditions for certain matrix operators on the spaces $\ell_p(T)$ and $\ell_\infty(T)$ to be compact, where $1\leq p

Kara, Emrah Evren/0000-0002-6398-4065; Ilkhan, Merve/0000-0002-0831-1474 WOS: 000439520400001 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.

In this paper, we introduce the class of generalized Stolz mappings. Also we prove that the class of $\ell ^{p}-$-type mappings is included in the class of generalized Stolz mappings and give a new quasinorm equivalent with $\Vert T\Vert_{\phi_{(p)}}$. Finally, we present some properties of the class of generalized Stolz mappings.

Kara, Emrah Evren/0000-0002-6398-4065 WOS: 000416101000006 In this paper, we introduce the notions of G-uniform continuity and G-Cauchy continuity of a function defined from one generalized metric space to another generalized metric space. Also, we investigate the relationships between these two types continuity and ordinary continuity. Further, we give some special properties of G-Cauchy sequences and G-totally bounded sets.

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 α-,β-,γ- 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, α-,β-,γ- 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. 68