Approximation by Kantorovich form of modified Szász–Mirakyan operators

Dhamija, Minakshi; Pratap, Ram; Deo, Naokant

doi:10.1016/j.amc.2017.09.004

Cited by 14 publications

(11 citation statements)

References 15 publications

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“…Proof. Our approach follows a route similar to the proof that appears in [6,Theorem 3.2 ] aiming at a Kantorovich modification for Szász-Mirakjan operators based on Jain and Pethe operators [9]. At first we define the operators E…”

Section: Theorem 32 Let the Operators Dmentioning

confidence: 99%

Kantorovich-type operators associated with a variant of Jain operators

Agratini

Doğru

2021

Stud. Univ. Babes-Bolyai Math.

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"This note focuses on a sequence of linear positive operators of integral type in the sense of Kantorovich. The construction is based on a class of discrete operators representing a new variant of Jain operators. By our statements, we prove that the integral family turns out to be useful in approximating continuous signals de ned on unbounded intervals. The main tools in obtaining these results are moduli of smoothness of rst and second order, K-functional and Bohman- Korovkin criterion."

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Section: Theorem 32 Let the Operators Dmentioning

confidence: 99%

Kantorovich-type operators associated with a variant of Jain operators

Agratini

Doğru

2021

Stud. Univ. Babes-Bolyai Math.

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“…In past years, there have been several modifications of operators to enhance their convergence and error estimation process (see previous studies 6‐8 ). In 2003, King 9 presented a sequence of linear positive operators which approximated each continuous function on [0, 1] while preserving the test function x 2 .…”

Section: Introductionmentioning

confidence: 99%

On the preservation of functions with exponential growth by modified Ismail–May operators

Mishra

Deo

2021

Math Methods in App Sciences

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In this study, our aim is to provide a modification of the so‐called Ismail–May operators that preserve exponential functions eAx,.7emA.5em∈.5emℝ. In support of this, we begin by estimating the convergence rate of the operators in terms of usual and exponential modulus of continuity. We also provide a global approximation and a quantitative Voronovskaya result. Moreover, to validate the modification, we exhibit some graphical representations using Mathematica software to compare the original operator and its modification. We conclude that the modified operators not only preserve exponential functions but also provide faster rate of convergence for A > 0.

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“…Szãsz in 1950, generalized the Bernstein sequence to approximate the space of continuous functions on the interval [0, ∞) as [16] S n (f ; x) = ∞ k=0 q n,k (x)f k n (1.2) where q n,k (x) = (nx) k k!e nx , x ∈ [0, ∞). Several new modifications of Szãsz sequence were constructed and studied, here we refer to [4,14,17,20]. Also,many authors have discussed the approximation behavior of different summation-integral type operators (see [6,7,10,12] )…”

Section: Introductionmentioning

confidence: 99%

Simultaneous Approximation of New Sequence of Integral Type Operators with Parameter Î´_0

Mohammad

Muslim

2019

Eur. J. Pure Appl. Math.

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In this paper, we define a new sequence of linear positive operators of integral type to approximate functions in the space,. First, we study the basic convergence theorem in simultaneous approximation and then study Voronovskaja-type asymptotic formula. Then, we estimate an error occurs by this approximation in the terms of the modulus of continuity. Next, we give numerical examples to approximate three test functions in the space by the sequence. Finally, we compare the results with the classical sequence of Szãsz operators on the interval . It turns out that, the sequence gives better than the results of the sequence for the two test functions using in the numerical examples.

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Approximation by Kantorovich form of modified Szász–Mirakyan operators

Cited by 14 publications

References 15 publications

Kantorovich-type operators associated with a variant of Jain operators

Kantorovich-type operators associated with a variant of Jain operators

On the preservation of functions with exponential growth by modified Ismail–May operators

Simultaneous Approximation of New Sequence of Integral Type Operators with Parameter Î´_0

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