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The idea of  I -convergence of real sequences was introduced by Kostyrko et al., (2000/01) and also independently by Nuray and Ruckle (2000). In this paper, we introduce the concepts of (Δ  m  ,  I )-statistical convergence of order  α  and strong (Δ  pm  ,  I )-Cesàro summability of order  α  of real sequences and investigated their relationship.

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On<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msup><mml:mi>Δ</mml:mi><mml:mi>m</mml:mi></mml:msup><mml:mo>,</mml:mo><mml:mi>I</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math>-Statistical Convergence of Order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:math>

On(Δm,I)-Statistical Convergence of Orderα