Abstract
A convolution in the variable exponent Lebesgue spaces $$L_{2\pi }^{p\left( \cdot \right) }$$ is defined and its basic properties are investigated. It is also proved that this convolution can be approximated in $$L_{2\pi }^{p\left( \cdot \right) }$$ by the finite linear combinations of Steklov means of the original function.
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