The paper aims to introduce Lagrangian and Hamiltonian formalism for mechanical systems using para/pseudo-Kähler manifolds, representing an interesting multidisciplinary field of research. Moreover, the geometrical, relativistical, mechanical and physical results related to para/pseudo-Kähler mechanical systems are given, too.

This paper deals with Weyl-Euler-Lagrange equations of motion on flat manifold. It is well known that a Riemannian manifold is said to be flat if its curvature is everywhere zero. Furthermore, a flat manifold is one Euclidean space in terms of distances. Weyl introduced a metric with a conformal transformation for unified theory in 1918. Classical mechanics is one of the major subfields of mechanics. Also, one way of solving problems in classical mechanics occurs with the help of the Euler-Lagrange equations. In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. Additionally, the improvements, obtained in this study, will be presented.

This paper aims to present Weyl–Euler–Lagrange and Weyl–Hamilton equations on [Formula: see text] which is a model of tangent manifolds of Constant W-Sectional Curvature. In this study some differential geometrical and physical results on the related Weyl-mechanical systems are given.

Euler-Lagrange and Hamilton equations on Kähler-Weyl manifolds were presented and the para-complex mathematical aspects of Lagrangian and Hamilton operator, dynamic equation, the action functional, Lagrangian and Hamilton's principle and equations and so on were given. The most important result revealed by this study, how to find the Lagrangian and Hamiltonian equations of motion without using the dynamic equations. For this, theorems were used as an alternative method of finding equations. As a result of this study, Weyl-Euler-Lagrange and Weyl-Hamilton partial differential equations were obtained for movement of objects on Kähler-Weyl manifolds.

In this paper, based on -convergence, we introduce the -core of sequences of complex numbers and determine a class of matrices A for which the -core(Ax) is a subset of Knopp's core for all bounded sequences x.