Ideal relatively uniform convergence with Korovkin and Voronovskaya types approximation theorems

DOI10.2298/FIL1914549MzbMath1499.40037MaRDI QIDQ5863970

Bipan Hazarika, Mohammed Ali Alghamdi, Syed Abdul Mohiuddine

Publication date: 3 June 2022

Published in: Filomat (Search for Journal in Brave)

zbMATH Keywords

Korovkin-type theoremVoronovskaya-type approximation theorem\((p, q)\)-Bernstein operatorsideal relatively uniform convergence

Mathematics Subject Classification ID

Convergence and divergence of series and sequences of functions (40A30) Rate of convergence, degree of approximation (41A25) Approximation by positive operators (41A36) Ideal and statistical convergence (40A35)

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Cites Work

• Unnamed Item
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• On Kantorovich modification of \((p,q) \)-Baskakov operators
• Statistical weighted \(A\)-summability with application to Korovkin's type approximation theorem
• Statistically relatively uniform convergence of positive linear operators
• On weighted statistical convergence based on \((p,q)\)-integers and related approximation theorems for functions of two variables
• Some weighted equi-statistical convergence and Korovkin type-theorem
• Weighted statistical convergence and its application to Korovkin type approximation theorem
• A Korovkin's type approximation theorem for periodic functions via the statistical summability of the generalized de la Vallée Poussin mean
• An application of almost convergence in approximation theorems
• \(\Lambda^{2}\)-weighted statistical convergence and Korovkin and Voronovskaya type theorems
• Erratum to: ``On (\(p, q\))-analogue of Bernstein operators
• Statistical convergence and ideal convergence for sequences of functions
• Statistical approximation results for Kantorovich-type operators involving some special polynomials
• Korovkin type approximation theorems obtained through generalized statistical convergence
• Some approximation theorems via statistical convergence.
• Generalized statistical convergence and convergence free spaces
• Deferred weighted \(\mathcal{A}\)-statistical convergence based upon the \((p, q)\)-Lagrange polynomials and its applications to approximation theorems
• Approximation by \((p,q)\)-Baskakov-Durrmeyer-Stancu operators
• Weighted equi-statistical convergence of the Korovkin type approximation theorems
• Statistical relatively equal convergence and Korovkin-type approximation theorem
• Statistical weighted \(\mathcal{B}\)-summability and its applications to approximation theorems
• Generalized statistically almost convergence based on the difference operator which includes the \((p,q)\)-gamma function and related approximation theorems
• Approximation by bivariate \((p,q)\)-Bernstein-Kantorovich operators
• Generalized equi-statistical convergence of the deferred Nörlund summability and its applications to associated approximation theorems
• \(\mathcal I\)-convergence
• Generalized equi-statistical convergence of positive linear operators and associated approximation theorems
• Generalized weighted statistical convergence and application
• On ideal equal convergence
• Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems
• Statistically and relatively modular deferred-weighted summability and Korovkin-type approximation theorems
• Korovkin type approximation theorem for BBH type operators via J-convergence
• On ideal convergence in probabilistic normed spaces
• Construction of a new family of Bernstein-Kantorovich operators
• A Korovkin type approximation theorems via $$\mathcal{I}$$ -convergence
• A certain class of weighted statistical convergence and associated Korovkin‐type approximation theorems involving trigonometric functions
• Some classes of ideal convergent sequences and generalized difference matrix operator
• Statistical (C,1) (E,1) summability and Korovkin’s theorem
• Some approximation results involving the q‐Szász–Mirakjan–Kantorovich type operators via Dunkl's generalization
• Approximation by bicomplex beta operators in compact ‐disks
• Sur la convergence statistique