A study on Fibo-Pascal sequence spaces and associated matrix transformations and applications of Hausdorff measure of non-compactness

In this article, we introduce Fibo-Pascal sequence spaces <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mi>P</m:mi> <m:mi>p</m:mi> <m:mi>F</m:mi> </m:msubsup> </m:math> {PₚF} , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mn>0</m:mn> <m:mo><</m:mo> <m:mi>p</m:mi> <m:mo><</m:mo> <m:mi mathvariant="normal">∞</m:mi> </m:mrow> </m:math> {0<p<∞} , and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mi>P</m:mi> <m:mi mathvariant="normal">∞</m:mi> <m:mi>F</m:mi> </m:msubsup> </m:math> {P∞F} through the utilization of the Fibo-Pascal matrix <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>P</m:mi> <m:mi>F</m:mi> </m:msup> </m:math> {PF} . We establish that both <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mi>P</m:mi> <m:mi>p</m:mi> <m:mi>F</m:mi> </m:msubsup> </m:math> {PₚF} and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mi>P</m:mi> <m:mi mathvariant="normal">∞</m:mi> <m:mi>F</m:mi> </m:msubsup> </m:math> {P∞F} are BK -spaces, enjoying a linear isomorphism with the classical spaces <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi mathvariant="normal">ℓ</m:mi> <m:mi>p</m:mi> </m:msub> </m:math> {ₚ} and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi mathvariant="normal">ℓ</m:mi> <m:mi mathvariant="normal">∞</m:mi> </m:msub> </m:math> {∞} , respectively. Further contributing to the depth of our investigation, we proceed to derive the Schauder basis of the space <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mi>P</m:mi> <m:mi>p</m:mi> <m:mi>F</m:mi> </m:msubsup> </m:math> {PₚF} , alongside an exhaustive computation of the α-, β-, and γ-duals for both spaces <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mi>P</m:mi> <m:mi>p</m:mi> <m:mi>F</m:mi> </m:msubsup> </m:math> {PₚF} and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mi>P</m:mi> <m:mi mathvariant="normal">∞</m:mi> <m:mi>F</m:mi> </m:msubsup> </m:math> {P∞F} . Additionally, we undertake the task of characterizing certain classes of matrix mappings pertaining to the spaces <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mi>P</m:mi> <m:mi>p</m:mi> <m:mi>F</m:mi> </m:msubsup> </m:math> {PₚF} and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mi>P</m:mi> <m:mi mathvariant="normal">∞</m:mi> <m:mi>F</m:mi> </m:msubsup> </m:math> {P∞F} . The final section of th