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- W3013651569 abstract "Abstract In this paper we consider a link $$B_{n,rho }$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>ρ</mml:mi></mml:mrow></mml:msub></mml:math> between Baskakov type operators $$B_{n,infty }$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math> and genuine Baskakov–Durrmeyer type operators $$ B_{n,1}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math> depending on a positive real parameter $$rho $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>ρ</mml:mi></mml:math> . The topic of the present paper is the pointwise limit relation $$left( B_{n,rho }fright) left( xright) rightarrow left( B_{n,infty }fright) left( xright) $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mfenced><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>ρ</mml:mi></mml:mrow></mml:msub><mml:mi>f</mml:mi></mml:mfenced><mml:mfenced><mml:mi>x</mml:mi></mml:mfenced><mml:mo>→</mml:mo><mml:mfenced><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:msub><mml:mi>f</mml:mi></mml:mfenced><mml:mfenced><mml:mi>x</mml:mi></mml:mfenced></mml:mrow></mml:math> as $$rho rightarrow infty $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>ρ</mml:mi><mml:mo>→</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:math> for $$xge 0.$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>x</mml:mi><mml:mo>≥</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo></mml:mrow></mml:math> As a main result we derive uniform convergence on each compact subinterval of the positive real axis for all continuous functions f of polynomial growth." @default.
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- W3013651569 date "2020-03-26" @default.
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- W3013651569 title "Convergence of linking Baskakov-type operators" @default.
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- W3013651569 doi "https://doi.org/10.1007/s10998-020-00337-y" @default.
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