Title: On λ-statistical convergence and strongly λ-summable functions of order α
Abstract: Abstract In this study, using the notion of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>(</mml:mo> <mml:mi>V</mml:mi> <mml:mo>,</mml:mo> <mml:mi>λ</mml:mi> <mml:mo>)</mml:mo> </mml:math> -summability and λ -statistical convergence, we introduce the concepts of strong <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>(</mml:mo> <mml:mi>V</mml:mi> <mml:mo>,</mml:mo> <mml:mi>λ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>p</mml:mi> <mml:mo>)</mml:mo> </mml:math> -summability and λ -statistical convergence of order α of real-valued functions which are measurable (in the Lebesgue sense) in the interval <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mi>∞</mml:mi> <mml:mo>)</mml:mo> </mml:math> . Also some relations between λ -statistical convergence of order α and strong <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>(</mml:mo> <mml:mi>V</mml:mi> <mml:mo>,</mml:mo> <mml:mi>λ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>p</mml:mi> <mml:mo>)</mml:mo> </mml:math> -summability of order β are given. MSC: 40A05, 40C05, 46A45.