The Journal of the Indian Mathematical Society

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Weighted β−absolute Convergence of Single and Double Walsh−Fourier Series of Functions of Φ − ∧ −BV


Affiliations
1 Department of Science and Humanities, Tatva Institute of Technological Studies, Arvalli, India
2 Department of Mathematics, The Maharaja Sayajirao University of Baroda, Vadodara, India
     

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For one variable function of Φ − ∧−bounded variation on [0,1] the sufficient condition for the weighted β−absolute convergence of its Walsh−Fourier series ∑m γm| ˆ f(m)|β, where 0 < β < 2 and {γm} is a weighted sequence, is obtained and is extended for two dimensional analogue.

Keywords

Absolute Convergence, Walsh−Fourier Series, Functions of φ − ∧−Bounded Variation.
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  • Weighted β−absolute Convergence of Single and Double Walsh−Fourier Series of Functions of Φ − ∧ −BV

Abstract Views: 416  |  PDF Views: 5

Authors

Kiran N. Darji
Department of Science and Humanities, Tatva Institute of Technological Studies, Arvalli, India
Rajendra G. Vyas
Department of Mathematics, The Maharaja Sayajirao University of Baroda, Vadodara, India

Abstract


For one variable function of Φ − ∧−bounded variation on [0,1] the sufficient condition for the weighted β−absolute convergence of its Walsh−Fourier series ∑m γm| ˆ f(m)|β, where 0 < β < 2 and {γm} is a weighted sequence, is obtained and is extended for two dimensional analogue.

Keywords


Absolute Convergence, Walsh−Fourier Series, Functions of φ − ∧−Bounded Variation.

References