Dual-hyperbolic Fibonacci and Lucas numbers

This thesis consists of four chapters. The first chapter is the introduction. The second part is divided into five sub-headings and basic concepts are given. In the first sub-headings, Fibonacci and Lucas numbers are introduced and necessary identities are given. In the second chapter, hyperbolic number system is introduced. In the third, dual number system is introduced and necessary theorems are given. In the fourth, quaternions are introduced and real quaternions are given as subheadings. In the fifth and last subheadings, dual-hyperbolic number system is introduced. The third section comprises the original part of thesis. In this section, dual-hyperbity Fibonacci and Lucas numbers are defined. In addition, subtraction and multiplication operations are given for these numbers and five different conjugates are defined for these numbers. Then, based on the generator function for Fibonacci numbers, generator function is obtained for dual hyperbolic Fibonacci numbers. Finally, the identities that are important for Fibonacci and Lucas numbers are defined for dual-hyperbolic Fibonacci and Lucas numbers. In the fourth chapter the general evaluation of thesis and recommendations for new researches are given.