Approximation Theorems for Functions of Two Variables via<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>σ</mml:mi></mml:mrow></mml:math>-Convergence
Approximation Theorems for Functions of Two Variables via<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>σ</mml:mi></mml:mrow></mml:math>-Convergence
Çakan et al. (2006) introduced the concept of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>σ</mml:mi></mml:mrow></mml:math>-convergence for double sequences. In this work, we use this notion to prove the Korovkin-type approximation theorem for functions of two variables by using the test functions 1,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>and construct an example by considering the …