@article{Yaying2025, 
author = {Taja Yaying and S. A. Mohiuddine and Jabr Aljedani},
title = {Exploring the    q-analogue of Fibonacci sequence spaces associated with    c and        c    0},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {1},
pages = {634-653},
keywords = {compactness, matrix mappings, q-Fibonacci sequence spaces, duals},
url = {https://www.sciopen.com/article/10.3934/math.2025028},
doi = {10.3934/math.2025028},
abstract = {We have proposed a    q-analogue    c  (      F    (  q  )  ) and        c    0    (      F    (  q  )  ) of Fibonacci sequence spaces, where        F    (  q  )  =  (      f          k      m        q    ) denotes a    q-Fibonacci matrix defined in the following manner:         f          k      m        q    =      {                                        q                          m              +              1                                                                          f                                  m                  +                  1                                            (              q              )                                                      f                                  k                  +                  3                                            (              q              )              −              1                                ,                          if          0          ≤          m          ≤          k          ,                                      0          ,                          if          m          >          k          ,                        for all    k  ,  m  ∈            Z        0    +  , where    (      f    k    (  q  )  ) denotes a sequence of    q-Fibonacci numbers. We developed a Schauder basis and determined several important duals (   α-,    β-,    γ-) of the aforesaid constructed spaces    c  (      F    (  q  )  ) and        c    0    (      F    (  q  )  ). Additionally, we examined certain characterization results for the matrix class    (      U    ,      V    ), where        U    ∈  {  c  (      F    (  q  )  )  ,      c    0    (      F    (  q  )  )  } and        V    ∈  {      ℓ          ∞        ,  c  ,      c    0    ,      ℓ    1    }. Essential conditions for the compactness of the matrix operators on the space        c    0    (      F    (  q  )  ) via the Hausdorff measure of noncompactness (Hmnc) were presented.}
}