Results 11 to 20 of about 80 (74)

Approximation by q-Post-Widder Operators Based on a New Parameter

Abstract and Applied Analysis
The purpose of this paper is to introduce q-Post–Widder operators based on a new parameter and study their approximation properties. The moments and central moments are investigated.
Qiu Lin
doaj   +2 more sources

Holmstedt's formula for the K‐functional: the limit case θ0=θ1$\theta _0=\theta _1$

Mathematische Nachrichten, Volume 296, Issue 12, Page 5474-5492, December 2023., 2023
Abstract We consider K‐interpolation spaces involving slowly varying functions, and derive necessary and sufficient conditions for a Holmstedt‐type formula to be held in the limiting case θ0=θ1∈{0,1}$\theta _0=\theta _1\in \lbrace 0,1\rbrace$. We also study the case θ0=θ1∈(0,1)$\theta _0=\theta _1\in (0,1)$.
Irshaad Ahmed, Alberto Fiorenza, Amiran Gogatishvili   +2 more
wiley   +1 more source

Some examples of equivalent rearrangement‐invariant quasi‐norms defined via f∗$f^*$ or f∗∗$f^{**}$

Mathematische Nachrichten, Volume 296, Issue 5, Page 1781-1802, May 2023., 2023
Abstract We consider Lorentz–Karamata spaces, small and grand Lorentz–Karamata spaces, and the so‐called L$\mathcal {L}$, R$\mathcal {R}$, LL$\mathcal {LL}$, LR$\mathcal {LR}$, RL$\mathcal {RL}$, and RR$\mathcal {RR}$ spaces. The quasi‐norms for a function f in each of these spaces can be defined via the nonincreasing rearrangement f∗$f^*$ or via the ...
Leo R. Ya. Doktorski, Pedro Fernández‐Martínez, Teresa Signes   +2 more
wiley   +1 more source

Traces of some weighted function spaces and related non‐standard real interpolation of Besov spaces

Mathematische Nachrichten, Volume 295, Issue 9, Page 1669-1689, September 2022., 2022
Abstract We study traces of weighted Triebel–Lizorkin spaces Fp,qs(Rn,w)$F^s_{p,q}(\mathbb {R}^n,w)$ on hyperplanes Rn−k$\mathbb {R}^{n-k}$, where the weight is of Muckenhoupt type. We concentrate on the example weight wα(x)=|xn|α$w_\alpha (x) = {\big\vert x_n\big\vert }^\alpha$ when |xn|≤1$\big\vert x_n\big\vert \le 1$, x∈Rn$x\in \mathbb {R}^n$, and ...
Blanca F. Besoy, Dorothee D. Haroske, Hans Triebel   +2 more
wiley   +1 more source

On interpolation of weakly compact bilinear operators

Mathematische Nachrichten, Volume 295, Issue 7, Page 1279-1291, July 2022., 2022
Abstract We study the interpolation properties of weakly compact bilinear operators by the real method and also by the complex method. We also study the factorization property of weakly compact bilinear operators through reflexive Banach spaces.
Fernando Cobos, Luz M. Fernández‐Cabrera, Antón Martínez   +2 more
wiley   +1 more source

Approximation Properties and q‐Statistical Convergence of Stancu‐Type Generalized Baskakov‐Szász Operators

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
In this article, we introduce Stancu‐type modification of generalized Baskakov‐Szász operators. We obtain recurrence relations to calculate moments for these new operators. We study several approximation properties and q‐statistical approximation for these operators.
Qing-Bo Cai, Adem Kilicman, Mohammad Ayman Mursaleen, Mikail Et   +3 more
wiley   +1 more source

New Results on the Equivalence of K‐Functionals and Modulus of Continuity of Functions Defined on the Sobolev Space Constructed by the Generalized Jacobi‐Dunkl Operator

Advances in Mathematical Physics, Volume 2022, Issue 1, 2022., 2022
In this paper, we establish some new generalized results on the equivalence of K‐functionals and modulus of continuity of functions defined on the Sobolev space Lα,β2ℝ, by using the harmonic analysis related to the Jacobi‐Dunkl operator Δα,β, where α ≥ β ≥ −1/2 and α ≠ −1/2.
Ali El Mfadel, Said Melliani, M’hamed Elomari, Mohammad Mirzazadeh   +3 more
wiley   +1 more source

Boundedness for the Modified Fractional Integral Operator from Mixed Morrey Spaces to the Bounded Mean Oscillation Space and Lipschitz Spaces

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
In this paper, we establish the boundedness of the modified fractional integral operator from mixed Morrey spaces to the bounded mean oscillation space and Lipschitz spaces, respectively.
Mingquan Wei, Lanyin Sun, Andrea Scapellato   +2 more
wiley   +1 more source

Approximation Properties of a New Type of Gamma Operator Defined with the Help of k‐Gamma Function

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
With the help of the k‐Gamma function, a new form of Gamma operator is given in this article. Voronovskaya type theorem, weighted approximation, rates of convergence, and pointwise estimates have been found for approximation features of the newly described operator.
Gurhan Icoz, Seda Demir, Yusuf Gurefe
wiley   +1 more source

Approximation of Functions by Dunkl‐Type Generalization of Szász‐Durrmeyer Operators Based on (p, q)‐Integers

Journal of Function Spaces, Volume 2021, Issue 1, 2021., 2021
In this article, our main purpose is to define the (p, q)‐variant of Szász‐Durrmeyer type operators with the help of Dunkl generalization generated by an exponential function. We estimate moments and establish some direct results of the aforementioned operators. Moreover, we establish some approximation results in weighted spaces.
Abdullah Alotaibi, Tuncer Acar
wiley   +1 more source