Trigonometric Approximation of Functions from $$L_{2\pi }^{p(x)}$$
Trigonometric Approximation of Functions from $$L_{2\pi }^{p(x)}$$
Abstract We generalize and improve the results of A. Guven, D. Israfilov, Xh. Z. Krasniqi and T. N. Shakh-Emirov. We consider the general methods of summability of Fourier series of functions from $$L_{2\pi }^{p(x)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>L</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msubsup></mml:math> with $$ p\left( x\right) \ge 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi><mml:mfenced><mml:mi>x</mml:mi></mml:mfenced><mml:mo>≥</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> . For estimate of the error …