Q−Fibonacci sequence spaces and q−Fibonacci statistical convergence

This thesis consists of five chapters. In the first chapter, the historical development of the thesis subject and the purpose of the thesis are emphasized by giving general information. In the second part, some basic definitions and theorems are given to clarify the findings part. In the third section, the sequence spaces $\ell_{p}(\widehat{F}_{q})$, $\ell_{\infty}(\widehat{F}_{q})$, $c(\widehat{F}_{q})$ and $c_{0}(\widehat{F}_{q})$ defined by $q-$Fibonacci band matrix and some inclusion relations are given. Topological and some geometrical properties of $\ell_{p}(\widehat{F}_{q})$ space are given. In the fourth section, $q-$Fibonacci statistical convergence is defined and the subject is discussed in terms of summability. In the fifth and last section, the results are briefly evaluated and suggestions are made for future studies.