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Uniform Statistical Convergence on Time Scales

Uniform Statistical Convergence on Time Scales

We will introduce the concept of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:math>- and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mo stretchy="false">(</mml:mo><mml:mi>λ</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-uniform density of a set and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:math>- and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mo stretchy="false">(</mml:mo><mml:mi>λ</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-uniform statistical convergence on an arbitrary time scale. However, we will define<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:math>-uniform Cauchy function on a time scale. Furthermore, some relations about these new …