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On the ๐ฟ1-Convergence of Modified Cosine Sums
-
Karanvir Singh
and Kulwinder Kaur
Published/Copyright:
March 10, 2010
Abstract
Concerning the ๐ฟ1-convergence of modified cosine sums introduced by Kumari and Ram [Indian J. Pure Appl. Math. 19: 1101โ1104, 1988], we generalise the results of Kumari, Ram [Indian J. Pure Appl. Math. 19: 1101โ1104, 1988] and Bor [Proc. Indian Acad. Sci. Math. Sci. 102: 235โ238, 1992]. Also a necessary and sufficient condition for the ๐ฟ1-convergence of cosine series has been deduced as a corollary for the said class.
Key words and phrases:: ๐ฟ1-convergence; quasi-monotone; modified cosine sums; Dirichlet's kernel; Fejรฉr kernel
Received: 2006-06-26
Revised: 2007-06-18
Published Online: 2010-03-10
Published in Print: 2008-March
ยฉ Heldermann Verlag
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Keywords for this article
๐ฟ1-convergence;
quasi-monotone;
modified cosine sums;
Dirichlet's kernel;
Fejรฉr kernel
Articles in the same Issue
- Functional Equations and ฮผ-Spherical Functions
- On the Uniqueness of Meromorphic Functions That Share Two Sets
- Convergence of the Ishikawa Iterates for Multi-Valued Mappings in Convex Metric Spaces
- The Existence of Solutions for Nonlinear Operator Equations
- A Measure Theoretical Version of the Aleksandrov Theorem
- Coincidence and Fixed Points of Contractive Type Multivalued Maps
- On the ๐ฟ1-Convergence of Modified Cosine Sums
- On the Approximation Properties of a Class of Convolution Type Nonlinear Singular Integral Operators
- A Metric Deformation to Obtain a Positive/Negative Gaussian Curvature on a Disk
- On Automorphism Groups of ฯ-Trees
- Growth and Approximation of Entire Harmonic Functions in ๐ ๐, ๐ > 3
- On Some Properties of the Dirichlet Problem at Resonance
- Grรถbner Bases for the Modules Over Noetherian Polynomial Commutative Rings
- Singular 2D Behaviors: Homologies
- Integrating Over the Inverse Image of Functions in the Besov Space
- The Fourth Order of Accuracy Decomposition Scheme for Abstract Hyperbolic Equation
- On a Generalization of Partial Isometries in Banach Spaces
- A Generalized Mandelbrot Set of Polynomials of Type ๐ธ๐ for Bicomplex Numbers