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In this paper, we establish a novel category of sequence spaces ℓ p q λ and ℓ ∞ q λ by utlizing q-analogue Λ q of Λ-matrix. Our investigation outlines several topological characteristics and inclusion results of these newly introduced sequence spaces, specifically identifying them as BK-spaces. Subsequently, we demonstrate that these novel sequence spaces are of nonabsolute type and establish their isometric isomorphism with ℓ p and ℓ ∞ . Moreover, we obtain the α-, β-, and γ-duals of these sequence spaces. We further characterize the class (ℓ p q λ , X) of matrices, where X is any of the spaces ℓ ∞ , c, or c 0 . Lastly, our study delves into the exploration of specific geometric properties exhibited by the space ℓ p q λ . [ABSTRACT FROM AUTHOR]

The main object of this paper is to construct a new class of modified (p , q) -Gamma-type operators. For this new class of operators, in section one, the general moments are find; in section two, the Korovkin-type theorem and some direct results are proved by considering the modulus of continuity and modulus of smoothness and their behavior in Lipschitz-type spaces. In section three, some results in the weighted spaces are given, and in the end, some shape-preserving properties are proven. [ABSTRACT FROM AUTHOR]

In this paper, we have proved certain kinds of Tauberian theorems for Nörlund-Cesáro summability methods in m-normed space X in statistically sense. We give necessary and sufficient Tauberian condition for this method of summability, in statistically sense. Also, we prove that Tauberian theorems under these summability methods are valid under oscillating slow condition of Schmidt-type and Hardy-type conditions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we will show Tauberian conditions under which ordinary convergence of the sequence (xn) in 2-normed space X, follows from Tp,qn-summability. In fact we give a necessary and sufficient Tauberian condition for this method of summability. Also, we prove that Tauberian Theorems for these summability methods are valid with Schmidt-type slowly oscillating condition as well as with Hardy-type "big O" condition. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we study the Kantorovich-Stancu-type generalization of Szász-Mirakyan operators including Brenke-type polynomials and prove a Korovkin-type theorem via the T -statistical convergence and power series summability method. Moreover, we determine the rate of the convergence. Furthermore, we establish the Voronovskaya- and Grüss-Voronovskaya-type theorems for T -statistical convergence. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new class of operators which will be called the class of k-quasi-class A(s, t) operators. An operator T ∈ B(H) is said to be k-quasi-class A(s, t) if T*k((|T|*t|T|2s|T*|t)1/t+s-|T*|2t)Tk≥ 0, where s > 0, t > 0 and k is a natural number. We show that an algebraically k-quasi-class A(s, t) operator T is polaroid, has Bishop’s property β and we prove that Weyl type theorems for k-quasi-class A(s, t) operators. In particular, we prove that if T* is algebraically k-quasi-class A(s, t), then the generalized a-Weyl’s theorem holds for T. Using these results we show that T* satisfies generalized the Weyl’s theorem if and only if T satisfies the generalized Weyl’s theorem if and only if T satisfies Weyl’s theorem. We also examine the hyperinvariant subspace problem for k-quasi-class A(s, t) operators. [ABSTRACT FROM AUTHOR]

Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce a new class of operators: (n, fc)-quasi class Q operators, superclass of (n, fc)-quasi paranormal operators. An operator T is said to be (n, fc)-quasi class Q if it satisfies ... for all X H and for some nonnegative integers n and k. We prove the basic structural properties of this class of operators. It will be proved that If T has a no non-trivial invariant subspace, then the nonnegative operator ... is a strongly stable contraction. In section 4, we give some examples which compare our class with other known classes of operators and as a consequence we prove that (n, fc)-quasi class Q does not have SVEP property. In the last section we also characterize the (n, fc)-quasi class Q composition operators on Fock spaces. [ABSTRACT FROM AUTHOR]

In this paper we will prove the Korovkin type theorem for new modified Szász-Mirakyan operators via A-statistical convergence and power summability method. Also we give the rate of the convergence related to the summability methods and in the last section we give a kind of Voronovskaya type theorem for A-statistical convergence and Grüss-Voronovskaya type theorem. [ABSTRACT FROM AUTHOR]

In this paper, we will show Tauberian theorems for the generalized de la Vallée-Poussin mean-convergent sequences of fuzzy numbers. [ABSTRACT FROM AUTHOR]

In this paper, we will show a new Tauberian theorems defined by weighted Nörlund-Cesáro summability method. [ABSTRACT FROM AUTHOR]

We will define the second order Cesaro operator spaces and we will show that those spaces are Banach spaces, are separable, fulfill dominant Lebesgue theorem, are not rearrangement invariant, not reflexive and strictly convex. [ABSTRACT FROM AUTHOR]

In this paper, we will show Tauberian conditions under which λstatistical convergence follows from (V,λ)-statistical convergence. Our results generalize the ones given in [3]. [ABSTRACT FROM AUTHOR]

This paper deals with some classes of bounded linear operators on Hilbert spaces. The main emphasis is put onto the classes A(k*) and A(k*)P; k > 0. Some additional results are given for other classes, like PA(k*), M - A(k*) and spectral properties of operators belonging to A(k*) are considered. We also describe under what conditions a matrix-operator TA;B belongs to A(k*), A(k*)P or PA(k*). [ABSTRACT FROM AUTHOR]

First, we will see that if T is a contraction of the k-quasi-∗-class A operator, then the nonnegative operator D = T∗k(∣T²∣ - ∣T∗∣²)Tk is a contraction whose power sequence {Dn}n=1∞ converges strongly to a projection P and TT∗kP = 0. Second, it will be proved that if T is a contraction of the k-quasi-∗-class A operator, then either T has a non-trivial invariant subspace or T is a proper contraction. Finally it will be proved that if T belongs to the k-quasi-∗-class A and is a contraction, then T has a Wold-type decomposition and T has the PF property. [ABSTRACT FROM AUTHOR]

In this paper criterion for L1-convergence of a certain cosine sums with quasi hyper-convex coefficients is obtained. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of operators, called k-quasi class A n* operators, which is a superclass of hyponormal operators and a subclass of (n, k)-quasi-*-paranormal operators. We will show basic structural properties and some spectral properties of this class of operators. We show that, if T is k-quasi class An* then ... Also, we will prove Browder's theorem and a-Browders theorem for k-quasi class An* operator. [ABSTRACT FROM AUTHOR]

We introduce the spaces of A(λ)-null, A(λ)-convergent, and A(λ)-bounded sequences. We examine some topological properties of the spaces and give some inclusion relations concerning these sequence spaces. Furthermore, we compute α-, β-, and γ-duals of these spaces. Finally, we characterize some classes of matrix transformations fromthe spaces of A(λ)-bounded and A(λ)-convergent sequences to the spaces of bounded, almost convergent, almost null, and convergent sequences and present a Steinhaus type theorem. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate a new class of the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators, which considerably extends the well-known class of the classical Baskakov-Schurer-Szász-Stancu approximation operators. For this new class of approximation operators, we present a Korovkin type theorem and a Grüss-Voronovskaya type theorem, and also study the rate of its convergence. Moreover, we derive several results which are related to the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators in the weighted spaces. Finally, we prove some shape-preserving properties for the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators and, as a special case, we deduce the corresponding shape-preserving properties for the classical Baskakov-Schurer-Szász-Stancu approximation operators. [ABSTRACT FROM AUTHOR]