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Our purpose in this paper is to extend the fixed point results of a <inline-formula> <math display="inline"> <semantics> <mrow> <mi>&#968;</mi> <mi>F</mi> </mrow> </semantics> </math> </inline-formula>-contraction introduced by Secelean N.A. and Wardowski D. (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>&#968;</mi> <mi>F</mi> </mrow> </semantics> </math> </inline-formula>-Contractions: Not Necessarily Nonexpansive Picard Operators, <i>Results. Math.</i><b>70</b>(3), 415&#8722;431 (2016)) defined on a metric space <i>X</i> into itself to the case of mapping defined on the product space <inline-formula> <math display="inline"> <semantics> <msup> <mi>X</mi> <mi>I</mi> </msup> </semantics> </math> </inline-formula>, where <i>I</i> is a set of positive integers (natural numbers). Some improvements to the conditions imposed on function <i>F</i> and space <i>X</i> are provided. An illustrative example is given.