On ari̇thmeti̇c functi̇ons and the tri̇gonometri̇c operators on them

In this thesis, firstly the definitions of logarithm and exponential operators defined by David Rearick were given and the relationships between these operators were explained. Then the features of the family of trigonometric operators were obtained by using these logarithms and exponential operators.New identitie for the family of new trigonometric operators were obtained considering the these trigonometric operators and elementary trigonometric and hyperbolic trigonometric function. Then logarithm and exponential operators defined by Trueman MacHenry for isobaric polynomials were described in detail and relationships between Fibonacci and Lucas polynomials defined by Trueman MacHenry was investigated by using these operators. Finally, some new identities were obtained by using these operators and hyperbolic trigonometric identities.