Generalized Weighted Invariant Mean Based on Fractional Difference Operator with Applications to Approximation Theorems for Functions of Two Variables

Kadak, Uğur

doi:10.1007/s00025-016-0634-8

Cited by 14 publications

(8 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For further studies one can investigate and generalize this results using sequence of modulus functions, Orlicz function, etc. One can obtain similar results by employing more generalized fractional difference operator as defined by Kadak in [24,25].…”

Section: Resultsmentioning

confidence: 68%

“…Many authors have introduced different classes of difference sequence spaces of fractional orders, obtained their , and duals and matrix transformations. Recently, Kadak [24] introduced the notions of statistically Ω-convergence and Ωstatistically convergence by the weighted method with respect to the fractional difference operator Δ , , . In his another work, Kadak [25] introduced the concepts of statistically weighted ,summability, weighted , -statistical converegence and weighted strongly ,summability with respect to a more generalized difference operator Δ , , , , including ( , )analogue of gamma function and obtained Korovkin type approximation theorems for function of two variables.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

On a Generalized Difference Sequence Spaces of Fractional Order associated with Multiplier Sequence Defined by A Modulus Function

Yaying¹

2020

Sakarya University Journal of Science

View full text Add to dashboard Cite

Let Γ() denotes the gamma function of a real number ∉ {0, −1, −2, … }. Then the difference matrix Δ of a fractional order is defined as (Δ) = ∑ (−1) () ! (). Using the difference operator Δ , we introduce paranormed difference sequence spaces (Δ , , Λ,) and (Δ , , Λ,) of fractional orders involving lacunary sequence, ; modulus function, and multiplier sequence, Λ = (). We investigate topological structures of these spaces and examine various inclusion relations.

show abstract

Section: Resultsmentioning

confidence: 68%

Section: Discussionmentioning

confidence: 99%

On a Generalized Difference Sequence Spaces of Fractional Order associated with Multiplier Sequence Defined by A Modulus Function

Yaying¹

2020

Sakarya University Journal of Science

View full text Add to dashboard Cite

show abstract

“…The theory of Korovkin type theorems was studied in several function spaces, and further details readers can find in those papers (see).…”

Section: Direct Estimatesmentioning

confidence: 99%

“…The theory of Korovkin type theorems was studied in several function spaces, and further details readers can find in those papers (see 1,2,5,9,12,[21][22][23][24]30 ). Now, we will prove the Korovkin type theorem for the generalized Szasz operators by multiple Appell polynomials by means of the power series method.…”

Section: Direct Estimatesmentioning

confidence: 99%

Approximation properties of the generalized Szasz operators by multiple Appell polynomials via power summability method

Braha

Kadak

2019

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper some properties of the generalized Szasz operators by multiple Appell polynomials are given, using into consideration the power summability method. In the first section are given some direct estimation related to the generalized Szasz operators by multiple Appell polynomials, including Korovkin type theorem. In the second section, we give some results related to the weighted spaces of continuous functions and Voronovskaya type theorem. In the third section, we have proved some results related to the statistical convergence of the generalized Szasz operators by multiple Appell polynomials, using into consideration the A− transformation. At the end of the paper are given some illustrative computational examples which make such summability methods (for example, power series method) more useful and fruitful for applications of functional analysis in approximation theory.

show abstract

“…They applied it first to construct the (p, q)-analogue of the classical Bernstein operators [18]. Most recently, the (p, q)-analogues of several operators and related approximation theorems has been studied extensively; see [1,2,3,4,7,10,11,12,16,17,21,22] and the references therein.…”

Section: Introduction-preliminariesmentioning

confidence: 99%

On (p,q)-analogue of divided differences and Bernstein operators

2017

J. Nonlinear Funct. Anal.

View full text Add to dashboard Cite

Abstract. In this paper, (p, q)-calculus is applied to construct (p, q)-analogue of divided differences. Another equivalent form of (p, q)-Bernstein operators which generalize the Phillips q-Bernstein polynomials are defined in terms of (p, q)-divided differences. It is shown that these operators reproduce constant as well as linear test functions. Further, we show that the difference of two consecutive (p, q)-Bernstein polynomials of a function f can be expressed in terms of second-order divided differences of f .

show abstract

Generalized Weighted Invariant Mean Based on Fractional Difference Operator with Applications to Approximation Theorems for Functions of Two Variables

Cited by 14 publications

References 27 publications

On a Generalized Difference Sequence Spaces of Fractional Order associated with Multiplier Sequence Defined by A Modulus Function

On a Generalized Difference Sequence Spaces of Fractional Order associated with Multiplier Sequence Defined by A Modulus Function

Approximation properties of the generalized Szasz operators by multiple Appell polynomials via power summability method

On (p,q)-analogue of divided differences and Bernstein operators

Contact Info

Product

Resources

About