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CONTINUITY OF FUZZY PROPER FUNCTIONS ON SOSTAK'S I-FUZZY TOPOLOGICAL SPACES
Roopkumar, Rajakumar,Kalaivani, Chandran Korean Mathematical Society 2011 대한수학회논문집 Vol.26 No.2
The relations among various types of continuity of fuzzy proper function on a fuzzy set and at fuzzy point belonging to the fuzzy set in the context of $\v{S}$ostak's I-fuzzy topological spaces are discussed. The projection maps are defined as fuzzy proper functions and their properties are proved.
RIDGELET TRANSFORM ON SQUARE INTEGRABLE BOEHMIANS
Roopkumar, Rajakumar Korean Mathematical Society 2009 대한수학회보 Vol.46 No.5
The ridgelet transform is extended to the space of square integrable Boehmians. It is proved that the extended ridgelet transform $\mathfrak{R}$ is consistent with the classical ridgelet transform R, linear, one-to-one, onto and both $\mathfrak{R}$, $\mathfrak{R}^{-1}$.1 are continuous with respect to $\delta$-convergence as well as $\Delta$-convergence.
Ridgelet transform on square integrable Boehmians
Rajakumar Roopkumar 대한수학회 2009 대한수학회보 Vol.46 No.5
The ridgelet transform is extended to the space of square integrable Boehmians. It is proved that the extended ridgelet transform R is consistent with the classical ridgelet transform R, linear, one-to-one, onto and both R, R^(-1) are continuous with respect to δ-convergence as well as Δ-convergence.
Ganesan, Chinnaraman,Roopkumar, Rajakumar Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.4
By introducing two fractional convolutions, we obtain the convolution theorems for fractional Fourier cosine and sine transforms. Applying these convolutions, we construct two Boehmian spaces and then we extend the fractional Fourier cosine and sine transforms from these Boehmian spaces into another Boehmian space with desired properties.
Fourier Cosine and Sine Transformable Boehmians
Ganesan, Chinnaraman,Roopkumar, Rajakumar Department of Mathematics 2014 Kyungpook mathematical journal Vol.54 No.1
The range spaces of Fourier cosine and sine transforms on $L^1$([0, ${\infty}$)) are characterized. Using Fourier cosine and sine type convolutions, Fourier cosine and sine transformable Boehmian spaces have been constructed, which properly contain $L^1$([0, ${\infty}$)). The Fourier cosine and sine transforms are extended to these Boehmian spaces consistently and their properties are established.