Approximation by Max-Product Type Operators

Abstract

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Conformable fractional approximation by max-product operators

“…We make Remark 4.16. Here we continue with the Max-product truncated sampling operators (see [4], p. 13) defined by such that x = x N,k , for any k ∈ {0, 1, ..., N } .…”

“…The authors in [4] studied similar such nonlinear operators such as: the Maxproduct Favard-Szász-Mirakjan operators and their truncated version, the Maxproduct Baskakov operators and their truncated version, also many other similar specific operators. The study in [4] is based on presented there general theory of sublinear operators. These Max-product operators tend to converge faster to the on hand function.…”

“…In this article we expand the study in [4] by considering conformable fractional smoothness of functions. So our inequalities are with respect to ω 1 (D n α f, δ), δ > 0, n ∈ N, where D n α f is the nth order conformable α-fractional derivative, α ∈ (0, 1], see [1], [6].…”

Approximation by truncated max‐product operators of Kantorovich‐type based on generalized (ϕ,ψ)‐kernels

“…Based on the Open Problem 5.5.4, pp. 324‐326 in Gal, in a series of papers, we have introduced and studied the so‐called max‐product operators attached to Bernstein polynomials, to Favard‐Szász‐Mirakjan operators, to Baskakov operators, to Meyer‐König and Zeller operators, to Bleimann‐Butzer‐Hahn operators and to linear sampling operators, see the recent research monograph …”

“…324-326 in Gal,22 in a series of papers, we have introduced and studied the so-called max-product operators attached to Bernstein polynomials, to Favard-Szász-Mirakjan operators, to Baskakov operators, to Meyer-König and Zeller operators, to Bleimann-Butzer-Hahn operators and to linear sampling operators, see the recent research monograph. 23 Very recent, the max-product idea was applied to approximation by Bernstein-Chlodowsky operators in Güngör and Ispir 24 and to weighted approximation by Favard operators in Holhos. 25 It is also worth mentioning that qualitative and quantitative approximation results for max-product neural networks operators were obtained in the recent papers.…”