On approximation of functions by some hump matrix means of Fourier series
-
Włodzimierz Łenski
and
Bogdan Szal
Abstract
The results corresponding to some theorems of S. Lal [Appl. Math. Comput. 209 (2009), 346–350] and the results of the authors [In: Banach Center Publ. 95, Polish Acad. Sci. Inst. Math., Warsaw, 2011, pp. 339–351] are shown. The same degrees of pointwise approximation as in mentioned papers by weaker assumptions on considered functions and examined summability methods are obtained. From presented pointwise results the estimation on norm approximation are derived. Some special cases as corollaries are also formulated.
References
[1] Lal, S.: Approximation of functions belonging to the generalized Lipschitz Class by C1Np summability method of Fourier series, Appl. Math. and Comput. 209 (2009), 346–350.10.1016/j.amc.2008.12.051Search in Google Scholar
[2] Leindler, L.: Integrability conditions pertaining to Orlicz space, J. Inequal. Pure and Appl. Math. 8 (2007), Art. 38, 6 pp.Search in Google Scholar
[3] Lenski, W.—Szal, B.: Approximation of functions from Lp(ω)β by general linear operators of their Fourier series, Banach Center Publ. 95 (2011), 339–351.10.4064/bc95-0-20Search in Google Scholar
[4] Lenski, W.—Szal, B.: Approximation of functions from Lp(ῶ)β by linear operators of conjugate Fourier series, Banach Center Publ., 92 (2011), 237–247.10.4064/bc92-0-16Search in Google Scholar
[5] Zygmund, A.: Trigonometric series, Cambridge, 2002.10.1017/CBO9781316036587Search in Google Scholar
© 2016 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- A triple representation of lattice effect algebras
- Periods of morgan-voyce sequences and elliptic curves
- Multiplicative generalized derivations on ideals in semiprime rings
- A few remarks on Poincaré-Perron solutions and regularly varying solutions
- Applications of extremal theorem and radius equation for a class of analytic functions
- On the “bang-bang” principle for a class of Riemann-Liouville fractional semilinear evolution inclusions
- New criteria for global exponential stability of linear time-varying volterra difference equations
- On approximation of functions by some hump matrix means of Fourier series
- Pseudo-amenability and pseudo-contractibility for certain products of Banach algebras
- Poisson kernels on semi-direct products of abelian groups
- Locally convex projective limit cones
- On the properties (wL) and (wV)
- On the existence of solutions for quadratic integral equations in Orlicz spaces
- Existence and uniqueness of best proximity points under rational contractivity conditions
- Almost Weyl structures on null geometry in indefinite Kenmotsu manifolds
- On the internal approach to differential equations 3. Infinitesimal symmetries
- A Characterization of the discontinuity point set of strongly separately continuous functions on products
- Wick differential and Poisson equations associated to the 𝚀𝚆𝙽-Euler operator acting on generalized operators
- Multivariate EIV models
- On codes over 𝓡k, m and constructions for new binary self-dual codes
- Domination number of total graphs
