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Öğe A New Modular Space Derived by Euler Totient Function(Murat TOSUN, 2019) İlkhan, Merve; Kara, Emrah Evren; Usta, FuatIn 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.Öğe Almost convergence and Euler totient matrix(Springer Basel Ag, 2020) Demiriz, Serkan; Ilkhan, Merve; Kara, Emrah EvrenThis paper is devoted to study the almost convergent sequence space c(F) derived by the Euler totient matrix. It is proved that the space c(F) and the space of all almost convergent sequences are linearly isomorphic. Further, the ss-dual of the space c(F) is determined and Euler totient core of a complex-valued sequence has been defined. Finally, inclusion theorems related to this new type of core are obtained.Öğe Approximation of functions by a new class of Gamma type operators; theory and applications(Ovidius Univ Press, 2024) Ozcelik, Reyhan; Kara, Emrah Evren; Usta, FuatThe study of the linear methods of approximation, which are given by sequences of positive and linear operators, studied extremely, in relation to different subjects of analysis, such as numerical analysis. The principal objective of this manuscript is to develop a new and more comprehensive version of Gamma type operators and presented their approximation features. For this purpose, we benefit from two sequences of functions, which are alpha(n)(x) and beta(n)(x), and from the function tau(x). To indicate how the function tau play a significant role in the construction of the operator, we reconstruct the mentioned operators which preserve exactly two test functions from the set {1, tau, tau(2)}. Then we established Voronovskaya type theorem and order of approximation properties of the newly defined operators utilizing weighted modulus of continuity to show that their approximation properties. At the end of this note, we present a series of numerical results to show that the new operators are an approximation technique.Öğe Approximation properties of a new family of Gamma operators and their applications(Springer, 2021) Özçelik, Reyhan; Kara, Emrah Evren; Usta, Fuat; Ansari, Khursheed J.The present paper introduces a new modification of Gamma operators that protects polynomials in the sense of the Bohman-Korovkin theorem. In order to examine their approximation behaviours, the approximation properties of the newly introduced operators such as Voronovskaya-type theorems, rate of convergence, weighted approximation, and pointwise estimates are presented. Finally, we present some numerical examples to verify that the newly constructed operators are an approximation procedure.Öğe BOURBAKI COMPLETENESS IN QUASI METRIC SPACES(Mathematical Research Press-Math Res, 2019) İlkhan, Merve; Kara, Emrah EvrenThe 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.Öğe Coincidence Point Theorems on $b$-Metric Spaces via $C_{F}$-Simulation Functions(Emrah Evren KARA, 2019) Özçelik, Reyhan; Kara, Emrah EvrenIn this paper, we investigate the existence and uniqueness of the coincidence points with the $C_{F}$-simulation function for two nonlinear operators on the $b$-metric space. Our results improve and generalize some of the results available in the literature.Öğe Compact Operators on Generalized Fibonacci Spaces(Amer Inst Physics, 2019) İlkhan, Merve; Usta, Fuat; Kara, Emrah EvrenThe 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.Öğe COMPACTNESS OF MATRIX OPERATORS ON SOME SEQUENCE SPACES DERIVED BY FIBONACCI NUMBERS(Univ Kragujevac, Fac Science, 2015) Kara, Emrah Evren; Başarır, Metin; Mursaleen, MohammadIn this paper, we apply the Hausdorff measure of noncompactness to obtain the necessary and sufficient conditions for certain matrix operators on the Fibonacci difference sequence spaces l(p)((F) over cap) and l(infinity)((F) over cap) to be compact, where 1 <= p < infinity.Öğe Editorial for special issue IECMSA 2020-International Eurasian Conference on Mathematical Sciences and Applications(Wiley, 2022) Tosun, Murat; Kara, Emrah Evren; Usta, Fuat[Bastract Not Available]Öğe FIXED POINTS OF (alpha, phi)-MEIR-KEELER CONTRACTIVE MAPPINGS IN GENERALIZED RECTANGULAR b-METRIC SPACES(Mili Publ, 2019) Ozcelik, Reyhan; Ilkhan, Merve; Kara, Emrah EvrenThe 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.Öğe Intuitionistic fuzzy I-convergent Fibonacci difference sequence spaces(Springeropen, 2019) Khan, Vakeel A.; Kara, Emrah Evren; Altaf, Henna; Khan, Nazneen; Ahmad, MobeenFibonacci difference matrix was defined by Kara in his paper (Kara in J. Inequal. Appl. 2013:38 2013). Recently, Khan et al. (Adv. Differ. Equ. 2018:199, 2018) using the Fibonacci difference matrix (F) over cap and ideal convergence defined the notion of c(0)(I)((F) over cap), c(I)((F) over cap) and l(infinity)(I) ((F) over cap). In this paper, we give the ideal convergence of Fibonacci difference sequence space in intuitionistic fuzzy normed space with respect to fuzzy norm (mu, nu). Moreover, we investigate some basic properties of the said spaces such as linearity, hausdorffness.Öğe Matrix transformations and compact operators on Catalan sequence spaces(Academic Press Inc Elsevier Science, 2021) Kara, Merve Ilkhan; Kara, Emrah EvrenThis paper is devoted to the study of domain of a recently defined conservative matrix in the spaces of p-absolutely summable sequences and bounded sequences. The aforementioned matrix is obtained by using the fascinating Catalan numbers. After determining the beta-duals of the newly defined Banach spaces, the characterization of some matrix operators are obtained. Finally, the characterization of certain compact operators is presented by utilizing the Hausdorff measure of non-compactness. (C) 2021 Elsevier Inc. All rights reserved.Öğe Multiplication operators on Cesàro second order function spaces(Birkhauser Verlag AG, 2019) İlkhan, Merve; Demiriz, Serkan; Kara, Emrah EvrenIn this article, we investigate bounded, invertible and compact multiplication operators on the second order Cesàro function spaces. © 2019, Springer Nature Switzerland AG.Öğe A NEW BANACH SPACE DEFINED BY EULER TOTIENT MATRIX OPERATOR(Element, 2019) İlkhan, Merve; Kara, Emrah EvrenThe 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.Öğe NEW BANACH SPACES DEFINED BY THE DOMAIN OF RIESZ-FIBONACCI MATRIX(Kangwon-Kyungki Mathematical Soc, 2021) Alp, Pınar Zengin; Kara, Emrah EvrenThe main object of this study is to introduce the spaces c(0)((F) over cap (q)) and c((F) over cap (q)) derived by the matrix (F) over cap (q) which is the multiplication of Riesz matrix and Fibonacci matrix. Moreover, we find the alpha-, beta-, gamma- duals of these spaces and give the characterization of matrix classes (Lambda((F) over cap (q)), Omega) and (Omega, Lambda((F) over cap (q))) for Lambda is an element of {c(0), c} and Omega is an element of {l(1), c(0), c, l(infinity)}.Öğe The new class L-z,L-p,L-E of s - type operators(Amer Inst Mathematical Sciences-Aims, 2019) Alp, Pınar Zengin; Kara, Emrah EvrenThe purpose, of this study is to introduce the class of s-type Z(u, v; l(p) (E)) operators, which we denote by L-z,L-p,L-E (X, Y), we prove that this class is an operator ideal and quasi-Banach operator ideal by a quasi-norm defined on this class. Then we define classes using other examples of s-number sequences. WC conclude by investigating which of these classes are injective, surjective or symmetric.Öğe A NEW CLASS OF OPERATOR IDEALS ON THE BLOCK SEQUENCE SPACE l(p) (E)(Mili Publ, 2018) Alp, Pınar Zengin; Kara, Emrah EvrenIn this study, we introduce the class of L-p, E type operators. Also, we show that the class L-p, E is a quasi-Banach operator ideal. Further, we de.ne a new class of operators L-phi(p), E by using L-p, E and symmetric norming function phi((p)).Öğe A New Paranormed Sequence Space Defined by Euler Totient Matrix(2019) İlkhan, Merve; Demiriz, Serkan; Kara, Emrah EvrenIn 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.Öğe A new regular infinite matrix defined by Jordan totient function and its matrix domain in l(p)(Wiley, 2021) Ilkhan, Merve; Simsek, Necip; Kara, Emrah EvrenIn this paper, we first define a new regular matrix by using the arithmetic function called Jordan totient function and study the matrix domain of this newly introduced matrix in the Banach space l(p). After computing the dual spaces of this new space, we characterize certain matrix mappings related to this space.Öğe A new type of statistical Cauchy sequence and its relation to Bourbaki completeness(Taylor & Francis As, 2018) İlkhan, Merve; Kara, Emrah EvrenBourbaki 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.
