In this paper, we construct the Chlodowsky-type Szász operators defined via Boas–Buck-type polyno... more In this paper, we construct the Chlodowsky-type Szász operators defined via Boas–Buck-type polynomials. We prove some approximation properties and obtain the rate of the convergence for these operators. We also study the Voronovskaya-type theorem and weighted approximation.
In this note we show that the Taylor series of a function in a weighted Dirichlet space is (gener... more In this note we show that the Taylor series of a function in a weighted Dirichlet space is (generalized) Nörlund summable, provided that the sequence determining the Nörlund operator is non-decreasing and has finite upper growth rate. In particular the Taylor series is Nörlund summable for all α > 1/2, and the rate of convergence is of the order O(n −1/2). The inequality α > 1/2 is sharp. On the other hand if the Taylor series is Nörlund summable and the partial sums of the determining sequence enjoy a certain growth condition then the determining sequence has finite lower growth rate. An analogue result is derived for a non-increasing sequence that is uniformly bounded away from zero.
In this paper, we study the Kantorovich variant of Chlodowsky Szász operators induced by Boas-Buc... more In this paper, we study the Kantorovich variant of Chlodowsky Szász operators induced by Boas-Buck type polynomials and prove a Korovkin type theorem. Also, we present the Voronovskaya type theorem and Grüss-Voronovskaya type theorem. In the last section, we estimate the rates of pointwise approximation of Kantorovich variant of Chlodowsky Szász operators induced by Boas-Buck type polynomials for functions with derivatives of bounded variation.
In this paper we study a notion called (E, 1)(C, 1)−weighted statistical convergence and prove a ... more In this paper we study a notion called (E, 1)(C, 1)−weighted statistical convergence and prove a Korovkin type approximation theorem. The rate of convergence for weighted statistical convergence is obtained. In the last section we also give Voronovskaya and Grüss‐Voronovskaya type theorems and some illustrative numerical examples
Let T be a bounded linear operator on a complex Hilbert space H. An operator T is called (n,k)-qu... more Let T be a bounded linear operator on a complex Hilbert space H. An operator T is called (n,k)-quasi class Q if it satisfies T (T k x) 2 1 n + 1 T 1+n (T k x) 2 + n T k x 2 , and (n,k)-quasi class Q * if it satisfies T * (T k x) 2 1 n + 1 T 1+n (T k x) 2 + n T k x 2 , for all x ∈ H and for some nonnegative integers n and k. In this paper, we will be studying the conditions under which composition operators and weighted composition operators on L 2 (μ) spaces become (n,k)-quasi class Q operators and (n,k)-quasi class Q * operators have been obtained in terms of Radon-Nikodym derivative h m. Some necessary and sufficient conditions for a composition operator C φ on Fock Spaces to be a (n,k)-quasi class Q operators and (n,k)-quasi class Q * operators have also been explored.
Boletim da Sociedade Paranaense de Matemática, 2021
$T\in L(H_{1}\oplus H_{2})$ is said to be an algebraic extension of a $\mathcal{A}^{*}_{n}$ opera... more $T\in L(H_{1}\oplus H_{2})$ is said to be an algebraic extension of a $\mathcal{A}^{*}_{n}$ operator if $$ T = \begin{pmatrix} T_{1} & T_{2} \\O & T_{3} \end{pmatrix} $$ is an operator matrix on $H_{1}\oplus H_{2}$, where $T_{1}$ is a $\mathcal{A}^{*}_{n}$ operator and $T_{3}$ is a algebraic.In this paper, we study basic and spectral properties of an algebraic extension of a $\mathcal{A}^{*}_{n}$ operator. We show that every algebraic extension of a $\mathcal{A}^{*}_{n}$ operator has SVEP, is polaroid and satisfies Weyl's theorem.
The main purpose of this paper is to use a power series summability method to study some approxim... more The main purpose of this paper is to use a power series summability method to study some approximation properties of Kantorovich type Szász–Mirakyan operators including Sheffer polynomials. We also establish Voronovskaya type result.
In this paper, we introduce a new class of operators: absolute-(k, m) paranormal operators. We wi... more In this paper, we introduce a new class of operators: absolute-(k, m) paranormal operators. We will show basic structural properties and some spectral properties of this class of operators. We will be studying the conditions under which composition operators and weighted composition operators on $$L^{2}(\mu )$$ spaces become absolute-(k, m)-paranormal operators and absolute- $$(k^{*},m)$$ -paranormal operators, in terms of Radon–Nikodym derivative $$h_{m}.$$ Some necessary and sufficient conditions for a composition operator $$C_{\phi }$$ on Fock Spaces to be an absolute-(1, m)-paranormal operators and absolute- $$(1^{*},m)$$ -paranormal operators have also been explored.
Hacettepe Journal of Mathematics and Statistics, 2018
In this paper, we introduce a new class of operators, called $m$-quasi class $\mathcal{A}(k^{*})$... more In this paper, we introduce a new class of operators, called $m$-quasi class $\mathcal{A}(k^{*})$ operators, which is a superclass of hyponormal operators and a subclass of absolute-$(k^{*},m)$-paranormal operators. We will show basic structural properties and some spectral properties of this class of operators. We show that if $T$ is $m$-quasi class $\mathcal{A}(k^{*})$, then $\sigma _{np}(T)\setminus \{0\}=\sigma _{p}(T)\setminus \{0\}$, $\sigma _{na}(T)\setminus \{0\}=\sigma _{a}(T)\setminus \{0\}$ and $T-\mu $ has finite ascent for all $\mu\in\mathbb{C}.$ Also, we consider the tensor product of $m$-quasi class $\mathcal{A}(k^{*})$ operators.
Fuzzy set theory has entered into a large variety of disciplines of sciences,technology and human... more Fuzzy set theory has entered into a large variety of disciplines of sciences,technology and humanities having established itself as an extremely versatileinterdisciplinary research area. Accordingly different notions of fuzzystructure have been developed such as fuzzy normed linear space, fuzzytopological vector space, fuzzy sequence space etc. While reviewing theliterature in fuzzy sequence space, we have seen that the notion of Tauberiantheorems for the Euler-N"{o}rlund mean-convergent sequences of fuzzy numbershas not been developed. In the present paper, we introduce some new conceptsabout statistical convergence of sequences of fuzzy numbers. The main purposeof this paper is to study Tauberian theorems for the Euler-N"{o}rlundmean-convergent sequences of fuzzy numbers and investigate some other kind ofconvergences named Euler-N"{o}rlund mean-level convergence so as to fill upthe existing gaps in the literature. The results which we obtained in thisstudy are much ...
In this paper we define the Cesáro second-order summability method for fuzzy numbers and prove Ko... more In this paper we define the Cesáro second-order summability method for fuzzy numbers and prove Korovkin type theorem, then as the application of it, we prove the rate of convergence. In the last section, we prove the kind of Voronovskaya type theorem and give some concluding remarks related to the obtained results. Mathematics Subject Classification (2010): 40A10, 40C10, 40E05, 40A05, 40G99, 26E50.
In this paper we will prove the Korovkin type theorem for modified Szász–Mirakyan operators via A... more In this paper we will prove the Korovkin type theorem for modified Szász–Mirakyan operators via A-statistical convergence and the power summability method. Also we give the rate of the convergence related to the above summability methods, and in the last section, we give a kind of Voronovskaya type theorem for A-statistical convergence and Grüss–Voronovskaya type theorem.
In this paper, we construct the Chlodowsky-type Szász operators defined via Boas–Buck-type polyno... more In this paper, we construct the Chlodowsky-type Szász operators defined via Boas–Buck-type polynomials. We prove some approximation properties and obtain the rate of the convergence for these operators. We also study the Voronovskaya-type theorem and weighted approximation.
In this note we show that the Taylor series of a function in a weighted Dirichlet space is (gener... more In this note we show that the Taylor series of a function in a weighted Dirichlet space is (generalized) Nörlund summable, provided that the sequence determining the Nörlund operator is non-decreasing and has finite upper growth rate. In particular the Taylor series is Nörlund summable for all α > 1/2, and the rate of convergence is of the order O(n −1/2). The inequality α > 1/2 is sharp. On the other hand if the Taylor series is Nörlund summable and the partial sums of the determining sequence enjoy a certain growth condition then the determining sequence has finite lower growth rate. An analogue result is derived for a non-increasing sequence that is uniformly bounded away from zero.
In this paper, we study the Kantorovich variant of Chlodowsky Szász operators induced by Boas-Buc... more In this paper, we study the Kantorovich variant of Chlodowsky Szász operators induced by Boas-Buck type polynomials and prove a Korovkin type theorem. Also, we present the Voronovskaya type theorem and Grüss-Voronovskaya type theorem. In the last section, we estimate the rates of pointwise approximation of Kantorovich variant of Chlodowsky Szász operators induced by Boas-Buck type polynomials for functions with derivatives of bounded variation.
In this paper we study a notion called (E, 1)(C, 1)−weighted statistical convergence and prove a ... more In this paper we study a notion called (E, 1)(C, 1)−weighted statistical convergence and prove a Korovkin type approximation theorem. The rate of convergence for weighted statistical convergence is obtained. In the last section we also give Voronovskaya and Grüss‐Voronovskaya type theorems and some illustrative numerical examples
Let T be a bounded linear operator on a complex Hilbert space H. An operator T is called (n,k)-qu... more Let T be a bounded linear operator on a complex Hilbert space H. An operator T is called (n,k)-quasi class Q if it satisfies T (T k x) 2 1 n + 1 T 1+n (T k x) 2 + n T k x 2 , and (n,k)-quasi class Q * if it satisfies T * (T k x) 2 1 n + 1 T 1+n (T k x) 2 + n T k x 2 , for all x ∈ H and for some nonnegative integers n and k. In this paper, we will be studying the conditions under which composition operators and weighted composition operators on L 2 (μ) spaces become (n,k)-quasi class Q operators and (n,k)-quasi class Q * operators have been obtained in terms of Radon-Nikodym derivative h m. Some necessary and sufficient conditions for a composition operator C φ on Fock Spaces to be a (n,k)-quasi class Q operators and (n,k)-quasi class Q * operators have also been explored.
Boletim da Sociedade Paranaense de Matemática, 2021
$T\in L(H_{1}\oplus H_{2})$ is said to be an algebraic extension of a $\mathcal{A}^{*}_{n}$ opera... more $T\in L(H_{1}\oplus H_{2})$ is said to be an algebraic extension of a $\mathcal{A}^{*}_{n}$ operator if $$ T = \begin{pmatrix} T_{1} & T_{2} \\O & T_{3} \end{pmatrix} $$ is an operator matrix on $H_{1}\oplus H_{2}$, where $T_{1}$ is a $\mathcal{A}^{*}_{n}$ operator and $T_{3}$ is a algebraic.In this paper, we study basic and spectral properties of an algebraic extension of a $\mathcal{A}^{*}_{n}$ operator. We show that every algebraic extension of a $\mathcal{A}^{*}_{n}$ operator has SVEP, is polaroid and satisfies Weyl's theorem.
The main purpose of this paper is to use a power series summability method to study some approxim... more The main purpose of this paper is to use a power series summability method to study some approximation properties of Kantorovich type Szász–Mirakyan operators including Sheffer polynomials. We also establish Voronovskaya type result.
In this paper, we introduce a new class of operators: absolute-(k, m) paranormal operators. We wi... more In this paper, we introduce a new class of operators: absolute-(k, m) paranormal operators. We will show basic structural properties and some spectral properties of this class of operators. We will be studying the conditions under which composition operators and weighted composition operators on $$L^{2}(\mu )$$ spaces become absolute-(k, m)-paranormal operators and absolute- $$(k^{*},m)$$ -paranormal operators, in terms of Radon–Nikodym derivative $$h_{m}.$$ Some necessary and sufficient conditions for a composition operator $$C_{\phi }$$ on Fock Spaces to be an absolute-(1, m)-paranormal operators and absolute- $$(1^{*},m)$$ -paranormal operators have also been explored.
Hacettepe Journal of Mathematics and Statistics, 2018
In this paper, we introduce a new class of operators, called $m$-quasi class $\mathcal{A}(k^{*})$... more In this paper, we introduce a new class of operators, called $m$-quasi class $\mathcal{A}(k^{*})$ operators, which is a superclass of hyponormal operators and a subclass of absolute-$(k^{*},m)$-paranormal operators. We will show basic structural properties and some spectral properties of this class of operators. We show that if $T$ is $m$-quasi class $\mathcal{A}(k^{*})$, then $\sigma _{np}(T)\setminus \{0\}=\sigma _{p}(T)\setminus \{0\}$, $\sigma _{na}(T)\setminus \{0\}=\sigma _{a}(T)\setminus \{0\}$ and $T-\mu $ has finite ascent for all $\mu\in\mathbb{C}.$ Also, we consider the tensor product of $m$-quasi class $\mathcal{A}(k^{*})$ operators.
Fuzzy set theory has entered into a large variety of disciplines of sciences,technology and human... more Fuzzy set theory has entered into a large variety of disciplines of sciences,technology and humanities having established itself as an extremely versatileinterdisciplinary research area. Accordingly different notions of fuzzystructure have been developed such as fuzzy normed linear space, fuzzytopological vector space, fuzzy sequence space etc. While reviewing theliterature in fuzzy sequence space, we have seen that the notion of Tauberiantheorems for the Euler-N"{o}rlund mean-convergent sequences of fuzzy numbershas not been developed. In the present paper, we introduce some new conceptsabout statistical convergence of sequences of fuzzy numbers. The main purposeof this paper is to study Tauberian theorems for the Euler-N"{o}rlundmean-convergent sequences of fuzzy numbers and investigate some other kind ofconvergences named Euler-N"{o}rlund mean-level convergence so as to fill upthe existing gaps in the literature. The results which we obtained in thisstudy are much ...
In this paper we define the Cesáro second-order summability method for fuzzy numbers and prove Ko... more In this paper we define the Cesáro second-order summability method for fuzzy numbers and prove Korovkin type theorem, then as the application of it, we prove the rate of convergence. In the last section, we prove the kind of Voronovskaya type theorem and give some concluding remarks related to the obtained results. Mathematics Subject Classification (2010): 40A10, 40C10, 40E05, 40A05, 40G99, 26E50.
In this paper we will prove the Korovkin type theorem for modified Szász–Mirakyan operators via A... more In this paper we will prove the Korovkin type theorem for modified Szász–Mirakyan operators via A-statistical convergence and the power summability method. Also we give the rate of the convergence related to the above summability methods, and in the last section, we give a kind of Voronovskaya type theorem for A-statistical convergence and Grüss–Voronovskaya type theorem.
Uploads
Papers by Naim Braha