Akademik Veri Yönetim Sistemi
TURAN-Fundamental Sciences Symposium (TURAN25), İstanbul, Türkiye, 23 - 25 Haziran 2025, ss.34, (Özet Bildiri)
In this study, we investigate fundamental analytical concepts within the framework of split quaternions, focusing specifically on real-variable split quaternion-valued functions. Although the literature includes various studies on split quaternion-variable functions, the definitions and explanations of limit, continuity, and certain derivative concepts remain either sufficiently undeveloped or ambiguous. Addressing this gap, we define the concepts of limit, derivative, P-limit, P-derivative, and integral for split quaternion-valued functions of a real variable, and give several theorems with proofs, including a theorem that determines the conditions under which the classical limit and the P-limit coincide. Additionally, numerous examples are provided to explain the concepts of P-limit, P-derivative and integral of elementary functions in particular.