Özkan, Engin; Eser, Engin; Uysal, Mine

In this work, we introduce Balancing, Balancing-Lucas polynomials, and k-Balancing, k-Balancing-Lucas polynomials. We exhibit some important theorems: Cassini, Catalan, Vajda, d'Ocagne, and Honsberger identities for Balancing, BalancingLucas polynomials, and k-Balancing, k-Balancing-Lucas polynomials. We give the concepts of recurrence relation, characteristic equation, roots of the characteristic equation, Binet formula, and generating function for polynomials, which are important for number sequences.

Altunba, Murat

Let (M, g) be an n-dimensional Riemannian manifold and (T * M,g(-)) be its cotangent bundle with a metricg that generalizes Sasaki and Cheeger-Gromoll metrics. In this paper, we investigate the harmonicity of the canonical projection pi : (T * M,g(-)) -> (M, g), the harmonicity of 1-forms regarded as maps sigma : (M, g) -> (T * M,g) and the harmonicity of the identity maps I-1 : (T * M,g(-)) -> (T * M, (S) g) and I-2 : (T * M, (S) g) -> (T * M,g(-)), where (S)g is the Sasaki metric. Moreover, we consider the same problems on the unit cotangent bundle T (1) *M .

Kiziltug, Sezai; Dede, Mustafa; Ekici, Cumali

In this paper, we define tubular surface by using a Darboux frame instead of a Frenet frame. Subsequently, we compute the Gaussian curvature and the mean curvature of the tubular surface with a Darboux frame. Moreover, we obtain some characterizations for special curves on this tubular surface in a Galilean 3-space.

Alagoz, Osman; Gunduz, Birol; Akbulut, Sezgin

In this paper we prove that the M-iteration process converges strongly faster than S-iteration and Picard-S iteration processes. Moreover, the M- iteration process is faster than the S n iteration process with a sufficient condition for weak contractive mapping defined on a normed linear space. We also give two numerical reckoning examples to support our main theorem. For approximating fixed points, all codes were written in MAPLE (C) 2018 All rights reserved.