In this research article, we construct a new sequence of Baskakov–Stancu–Durrmeyer operators including the shape parameter $$\alpha$$
 and study the uniform convergence of these operators by means of modulus of continuity to the continuous functions h(u) on $$u\in [0,1]$$
 . We investigate the pointwise and weighted approximation in terms of Ditzian–Totik uniform with the aid of first and second order of modulus of smoothness. Further, we calculate the direct estimate of rate of convergence in terms of Lipschitz function. Next, we study weight approximation result.

Approximation Properties by Modified Baskakov–Durrmeyer Operators Based on Shape Parameter- $$\alpha$$ α

In this paper, we investigate the boundedness, compactness and essential norm of weighted composition operators between Zygmund-type spaces with normal weight. Mathematics subject classification (2010): 47B33, 30H10.

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Essential norm of weighted composition operators on Zygmund-type spaces with normal weight

The present paper emphasises on equi-statistical convergence, pointwise statistical convergence and uniform statistical convergence for a sequence of real-valued functions by using deferred Cesaro ...

Deferred Cesàro and deferred Euler equi-statistical convergence and its applications to Korovkin-type approximation theorem

In this paper, we give new essential norm estimates of weighted composition operators from into the Bloch space, where u is a function analytic on the unit disc and is an analytic self-map of . Moreover, a new characterization for the boundedness and compactness of the weighted composition operators is obtained by the nth power of the symbol and the Volterra operators and .

New essential norm estimates of weighted composition operators from H∞ into the Bloch space

In this paper, we introduce and study some strongly almost convergent double sequence spaces by Riesz mean associated with four-dimensional bounded regular matrix and a Musielak–Orlicz function ove...

Almost strongly orlicz double sequence spaces of regular matrices and their applications to statistical convergence

Recently, Korus [7] studied the ${\Lambda^{2}}$-strong convergence of numerical sequences. By using the idea of this paper, we introduce ${[\Lambda^{2}, F, u, p]}$-strongly convergent sequence spaces defined by a sequence of modulus functions. We also make an effort to study some inclusion relations, topological and geometric properties of these spaces. Some characterizations for strong convergent sequences are given. Finally, we study statistical convergence over these spaces and problems related to Fourier series.

Applications of strongly convergent sequences to Fourier series by means of modulus functions

Abstract In the present paper we characterize the compact, invertible, Fredholm and closed range weighted composition operators on Cesàro function spaces. We also make an effort to compute the essential norm of weighted composition operators.

Essential norm of weighted composition operators

We introduce new classes of generalized Orlicz-Garling sequences and Orlicz-Lorentz sequences by using a sequence of Orlicz functions and difference operator. We show that the Orlicz-Garling sequence space admits a unique 1-subsymmetric basis and a 1-dominated block basic sequence in $g(\mathcal{M},\Delta^{(m)}, v, p)$
 . We also make an effort to prove that every symmetric normalized block Orlicz-Garling sequence dominates an Orlicz-Lorentz sequence. Finally, we study some geometric properties of these spaces and establish some inclusion relations between spaces.

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Charu Sharma

Papers

Applications of strongly convergent sequences to Fourier series by means of modulus functions

Almost strongly orlicz double sequence spaces of regular matrices and their applications to statistical convergence

Essential norm of weighted composition operators

Orlicz-Garling sequence spaces of difference operator and their domination in Orlicz-Lorentz spaces.

Applications of Tauberian theorem in Orlicz spaces of double difference sequences of fuzzy numbers