<i>q</i> -Fibonacci statistical convergence

Abstract In this paper, we use the q -Fibonacci band matrix <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mover accent="true"> <m:mi>F</m:mi> <m:mo>^</m:mo> </m:mover> <m:mi>q</m:mi> </m:msub> <m:mo>=</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:msub> <m:mover accent="true"> <m:mi>F</m:mi> <m:mo>^</m:mo> </m:mover> <m:mrow> <m:mi>n</m:mi> <m:mo>⁢</m:mo> <m:mi>k</m:mi> </m:mrow> </m:msub> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>q</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {\widehat{F}_{q}=(\widehat{F}_{nk}(q))} to introduce the notions of q -Fibonacci summability, q -Fibonacci statistical convergence, strongly <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mover accent="true"> <m:mi>F</m:mi> <m:mo>^</m:mo> </m:mover> <m:mi>q</m:mi> </m:msub> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">[</m:mo> <m:mi>p</m:mi> <m:mo stretchy="false">]</m:mo> </m:mrow> </m:mrow> </m:math> {\widehat{F}_{q}[p]} -Cesàro summability and give some inclusion relations about these concepts.