Lupaş type Bernstein operators on triangles based on quantum analogue

In this paper, we define and study q-statistical limit point, q-statistical cluster point, q-statistically Cauchy, q-strongly Cesàro and statistically C1q-summable sequences. We establish relationships of q-statistical convergence with q-statistically Cauchy, q-strongly Cesàro and statistically C1q-summable sequences. Further, we apply q-statistical convergence to prove a Korovkin type approximation theorem.

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“…Proof. Since each of 1, υ, υ 2 belongs to C[0, 1], conditions ( 8)- (10) follow immediately from (7). Let ∈ C[0, 1].…”

Section: Application Of Q-statistical Convergencementioning

confidence: 99%

“…In approximation theory, it also plays a very important role; e.g., [7][8][9][10][11][12]. The q-analogs of Bernstein operators and other operators significantly lead to more general results on approximations and show a better rate of convergence than the respective classical operators [13].…”

Section: Introductionmentioning

confidence: 99%

Statistical Convergence via q-Calculus and a Korovkin’s Type Approximation Theorem

Mursaleen

Serra‐Capizzano

2022

Axioms

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“…Schumaker studied fitting surfaces to scattered data in [29]. For results related to Phillips and Lupaş type Bernstein operators on triangles, one can see recent work [10,11]. Approximation properties for Bernstein type polynomials and its remainder terms are evaluated by D. D Stancu in [30,31], R. Paltanea studied Durrmeyer type operators on a simplex in [16], A. Kajla and T. Acar studied blending type approximation by Bernstein durrmeyer type operators and α-Bernstein operators in [18,19].…”

Section: Introductionmentioning

confidence: 99%

Interpolation by Lupaş type operators on Tetrahedrons

2023

RNA

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The goal of this study is to build Lupaş type Bernstein operators (rational) on tetrahedrons with all straight edges and three curved edges determined by specific functions. Interpolation attributes, approximation accuracy (degree of exactness, precision set), and the remainders of the approximation formula of Lupaş type Bernstein operators are assessed using Peano's theorem and modulus of continuity.

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Iterates of q-Bernstein operators on triangular domain with all curved sides

Iliyas

Khan

Arif

et al. 2022

Demonstratio Mathematica

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In this article, Phillips-type Bernstein operators ( ℬ m , q t F ) ( t , s ) ({{\mathcal{ {\mathcal B} }}}_{m,q}^{t}F)\left(t,s) and ( ℬ n , q s F ) ( t , s ) ({{\mathcal{ {\mathcal B} }}}_{n,q}^{s}F)\left(t,s) , their products, and Boolean sum based on q-integer have been studied on a triangle with all curved sides. Furthermore, convergence of iterates of these operators have been analyzed using the weakly Picard operators technique and the contraction principle.

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Lupaş type Bernstein operators on triangles based on quantum analogue

Cited by 5 publications

References 10 publications

Statistical Convergence via q-Calculus and a Korovkin’s Type Approximation Theorem

Statistical Convergence via q-Calculus and a Korovkin’s Type Approximation Theorem

Interpolation by Lupaş type operators on Tetrahedrons

Iterates of q-Bernstein operators on triangular domain with all curved sides

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