Gamma operators reproducing exponential functions

Acar, Tuncer; Mursaleen, M.; Deveci, Serife Nur

doi:10.1186/s13662-020-02880-x

Cited by 18 publications

(14 citation statements)

References 18 publications

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“…The epsilon function given in Definition 1 may be treated as an alternative of the exponential function on the domain (−d, d). The exponential function has an extremely wide range of applications in many areas of science including mathematics, physics, chemistry, computer science, economics and biology (see, e.g., [19,1,4,15,5]). Our motivation was to generalize the epsilon function such that it can be used to approximate the exponential function with an even higher level of flexibility.…”

Section: Preliminariesmentioning

confidence: 99%

The Generalized Epsilon Function

Jónás

2022

Acta Cybern

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It is well known that the exponential function plays an extremely important role in many areas of science. In this study, a generator function-based mapping, called the generalized epsilon function is presented. Next, we demonstrate that the exponential function is an asymptotic generalized epsilon function. Exploiting this result and the fact that this new function is generator function-dependent, it can be utilized as a very flexible alternative to the exponential function in a wide range of applications. We should add that if the generator is a rational function, then the generalized epsilon function is rational as well. In this case, the generalized epsilon function is computationally simple and it may be treated as an easy-to-compute alternative to the exponential function. In this paper, we briefly present two applications of this novel function: an approximation to the exponential probability distribution, and an alternative to the sigmoid function on a bounded domain.

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Section: Preliminariesmentioning

confidence: 99%

The Generalized Epsilon Function

Jónás

2022

Acta Cybern

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“…For instance, Duman and Özarslan 10 gave a modification of classical Szász operators to provide a better error estimation, Ozsarac and Acar 11 presented a new modification of Baskakov operators, which preserve the functions e μt and e 2 μt , μ > 0, Bodur et al 12 introduced a general class of Baskakov–Szász–Stancu operators preserving exponential functions, and many more. Readers can refer to these recent articles and books 13‐18 for more such interesting papers related to this approach.…”

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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“…e −xy y n F p x, n y dy and investigated the approximation properties for differentiable functions in the polynomial weighted spaces. Recently, new operators have been defined by using the Gamma operator and the convergence properties of these operators are examined [1,6,10,21].…”

Section: Introductionmentioning

confidence: 99%

Approximation properties of modified Jain-Gamma operators

Erdoğan

Olgun

2021

Carpathian Math. Publ.

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In the present paper, we study some approximation properties of a modified Jain-Gamma operator. Using Korovkin type theorem, we first give approximation properties of such operator. Secondly, we compute the rate of convergence of this operator by means of the modulus of continuity and we present approximation properties of weighted spaces. Finally, we obtain the Voronovskaya type theorem of this operator.

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Gamma operators reproducing exponential functions

Cited by 18 publications

References 18 publications

The Generalized Epsilon Function

The Generalized Epsilon Function

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

Approximation properties of modified Jain-Gamma operators

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