Multiplikatif Jeodeziklerin Geometrisi

Yıl 2025, Cilt: 37 Sayı: 2, 55 - 63

Muhittin Evren Aydın , Esra Dilmen , Gülşah Yaman

Öz

Bu makalede R_*^n multiplikatif Öklid uzayın ve bu uzayda bulunan bazı multiplikatif yüzeylerin jeodezikleri araştırıldı. İlk olarak R_*^n uzayının jeodezikleri elde edildi. R_*^n uzayında multiplikatif silindirler ve multiplikatif koniler üzerindeki multiplikatif jeodezikler sınıflandırıldı. Son olarak multiplikatif helis yüzeyleri tanımlanıp multiplikatif jeodezikleri karakterize edildi.

Anahtar Kelimeler

Multiplikatif Öklid uzayı , multiplikatif silindir , multiplikatif koni , multiplikatif helis yüzeyi

Destekleyen Kurum

Türkiye Bilimsel ve Teknolojik Araştırma Kurumu (TÜBİTAK)

Teşekkür

Bu çalışma Türkiye Bilimsel ve Teknolojik Araştırma Kurumu (TÜBİTAK) 2209-A - Üniversite Öğrencileri Araştırma Projeleri Destekleme Programı tarafından desteklenmiştir. Yazarlar desteği için TÜBİTAK’ a teşekkürleri sunmaktadırlar.

Geometry of Multiplicative Geodesics

Öz

In this paper, the geodesics of the multiplicative Euclidean space R_*^n and some multiplicative surfaces in this space are investigated. First, the geodesics of the space R_*^n are obtained. The multiplicative geodesics on multiplicative cylinders and multiplicative cones in R_*^n are classified. Finally, multiplicative helix surfaces are defined, and their multiplicative geodesics are characterized.

Anahtar Kelimeler

Multiplicative Euclidean space , multiplicative cylinder , multiplicative cone , multiplicative helix surface

Kaynakça

• Grossman M, Katz R. Non-Newtonian Calculus. Lee Press, Massachussets, USA, 1972.
• Stanley D. A multiplicative calculus. Primus IX 1999; 4: 310–326.
• Georgiev SG. Multiplicative Differential Geometry. Chapman and Hall/CRC. New York, USA, 2022.
• Nurkan SK, Gurgil I, Karacan MK. Vector properties of geometric calculus. Math Meth Appl Sci 2023; 46: 17672–17691.
• Aydın ME, Has A, Yılmaz B. A non-Newtonian approach in differential geometry of curves: multiplicative rectifying curves. Bull Korean Math Soc 2024; 61(3): 849–866.
• Aydın ME, Has A, Yılmaz B. Multiplicative rectifying submanifolds of multiplicative Euclidean space. Math Meth Appl Sci 2025; 48: 329–339.
• Aniszewska D, Rybaczuk M. Analysis of the multiplicative Lorenz system. Chaos Solitons Fract 2005; 25(1): 79–90.
• Aniszewska D, Rybaczuk M. Lyapunov type stability and Lyapunov exponent for exemplary multiplicative dynamical systems. Nonlinear Dyn 2008; 54: 345–354.
• Cordova-Lepe F. The multiplicative derivative as a measure of elasticity in economics. TEMAT-Theaeteto Atheniensi Math 2006; 2(3): 7 sayfa.
• Filip DA, Piatecki C. A non-newtonian examination of the theory of exogenous economic growth. Math Aeterna 2014; 4: 101–117.
• Florack L, van Assen H. Multiplicative calculus in biomedical image analysis. J. Math Imaging Vis 2012; 42: 64–75.
• Mora M, Cordova-Lepe F, Del-Valle R. A non-Newtonian gradient for contour detection in images with multiplicative noise. Pattern Recogn Lett (2012); 33(10): 1245–1256.
• Bashirov AE, Kurpınar EM, Özyapıcı A. Multiplicative calculus and its applications. J Math Anal Appl 2008; 337: 36–48.
• Bashirov AE, Norozpour S. On an alternative view to complex calculus. Math Meth Appl Sci 2018; 41: 7313–7324.
• Uzer A. Multiplicative type complex calculus as an alternative to the classical calculus. Comp Math Appl 2010; 60(10): 2725–2737.
• Bashirov AE, Mısırlı E, Tandoğdu Y, Özyapıcı A. On modeling with multiplicative differential equations. Appl Math J Chinese Univ 2011; 26(4): 425–438.
• Waseem M, Noor MA, Shah FA, Noor KI. An efficient technique to solve nonlinear equations using multiplicative calculus. Turk J Math 2018; 42(2): 679–691.
• Yalçın N. The solutions of multiplicative Hermite differential equation and multiplicative Hermite polynomials. Rend Circ Mat Palermo II. Ser 2021; 70: 9–21.
• Mısırlı E, Gürefe Y. Multiplicative Adams Bashforth-Noulton methods. Numer Algor 2011; 57: 425–439.
• Özyapici A, Rıza M, Bilgehan B, Bashirov AE. On multiplicative and Volterra minimization methods. Numer Algor 2014; 67: 623–636.
• Yazıcı M, Selvitop H. Numerical methods for the multiplicative partial differential equations. Open Math 2017; 15: 1344–1350.
• Çakmak AF, Basar F. Some new results on sequence spaces with respect to non-Newtonian calculus. J Ineq Appl 2012; 228: 17 pages.
• Cordova-Lepe F, Del Valle R, Vilches K. A new approach to the concept of linearity. Some elements for a multiplicative linear algebra. Int J Comp Math 2020; 97(1-2): 109-119.
• Torres DFM. On a Non-Newtonian Calculus of Variations. Axioms 2020; 10: 171. https://doi.org/10.3390/axioms10030171
• Göktaş S, Kemaloğlu H, Yılmaz E. Multiplicative conformable fractional Dirac system. Turk J Math 2022; 46(3); 973–990.
• Gülşen T, Yılmaz E, Göktaş S. Multiplicative Dirac system. Kuwait J Sci 2022; 49(3): 1–11.
• Yılmaz E. Multiplicative Bessel equation and its spectral properties. Ricerche mat 2024; 73: 1289–1305.
• Georgiev SG, Zennir K. Multiplicative Differential Calculus. Chapman and Hall/CRC. New York, USA, 2022.
• Georgiev SG, Zennir K, Boukarou A. Multiplicative Analytic Geometry. Chapman and Hall/CRC. New York, USA, 2022.