Matematik Bölümü
http://hdl.handle.net/20.500.11787/59
Matematik Bölümünü içerir.2024-03-29T15:18:43ZOn A new class of hyperbolic fibonacci functions via some special polynomials
http://hdl.handle.net/20.500.11787/8366
On A new class of hyperbolic fibonacci functions via some special polynomials
Köme, Sure; Yazlık, Yasin
In recent years, many researchers have studied hyperbolic Fibonacci functions and some special polynomials, which are important areas of mathematics. In this study, we give an extension of the Euler polynomials in order to obtain the correlation between the hyperbolic Fibonacci functions and Euler polynomials. We define symmetrical Fibonacci sine and symmetrical Fibonacci cosine functions for some special Euler polynomials. Moreover, we derive new identities for these types of symmetrical Fibonacci functions by using analytical techniques.
2023-06-08T00:00:00ZSome properties of the conditional dual lucas octonions
http://hdl.handle.net/20.500.11787/8365
Some properties of the conditional dual lucas octonions
Köme, Sure
The study of higher-dimensional algebraic structures has gained significant attention in recent
years. Octonions, a normed division algebra with eight dimensions, have applications in fields such as
quantum logic, special relativity and string theory. In this study, we introduce the conditional dual Lucas
octonions. Also, we investigate several important properties and characteristics of these octonions.
Firstly, we establish the algebraic structure of the conditional dual Lucas octonions, providing a
comprehensive definition and outlining their fundamental mathematical properties. Furthermore, we
obtain generating functions, the Binet formulas, Catalan's identities, and Cassini's identities of the
conditional dual Lucas octonions. Through our analysis and exploration, we contribute to the
understanding of the conditional dual Lucas octonions, shedding light on their algebraic properties. This
study ensures a comprehensive overview of the generalization of the various octonions.
2023-07-10T00:00:00ZOn the generalized fibonacci matrix hybrinomials
http://hdl.handle.net/20.500.11787/8364
On the generalized fibonacci matrix hybrinomials
Köme, Sure; Yazan, Sefa
Complex numbers, hyperbolic numbers, and dual numbers are well-known number systems in the literature. The hybrid numbers, which have significantly increased interest in recent years, are the generalization of complex numbers, hyperbolic numbers, and dual numbers. Until now, many researchers have studied the geometric and physical applications of hybrid numbers and the Fibonacci numbers which arise in the applications of mathematics, computer science, physics, biology, and statistics. In addition, there are many studies on the matrix sequences of the Fibonacci numbers. In this study, we define the generalized Fibonacci matrix hybrinomials with the help of the generalized Fibonacci polynomials. We also provide the Binet formula and generating function of the generalized Fibonacci matrix hybrinomials. Finally, we give some summation formulas with the help of the Binet formula.
2022-11-10T00:00:00ZSome properties of generalized bivariate bihyperbolic polynomials
http://hdl.handle.net/20.500.11787/8344
Some properties of generalized bivariate bihyperbolic polynomials
Köme, Sure; Ergezer, Sinem
Understanding the properties and applications of bihyperbolic polynomials sheds light on many mathematical problems. For this reason, bihyperbolic polynomials can play an important role in various fields of mathematics. Therefore, there has been an increase in studies on bihyperbolic polynomials recently. On the other hand, bivariate polynomials, used to represent relationships between two variables, can appear in a variety of forms and are used in many scientific disciplines. In this study, some generalized bivariate bihyperbolic polynomials will be discussed. First, when defining these bihyperbolic polynomials, definitions, theorems and properties existing in the literature will be utilized. After new definitions are obtained, the generaitng functions of generalized bivariate bihyperbolic polynomials will be obtained in different methods. Subsequently, properties related to these polynomials will be discussed. All these results are expected to further solidify the position of generalized bivariate bihyperbolic polynomials in the mathematical literature and contribute to future research in this field.
2023-11-11T00:00:00Z