Matrix methods are a useful tool while dealing with many problems stemming from linear recurrence relations. In this paper, we discuss factorizations and inverse of two kinds generalized k-Fibonacci matrices. We derive some identities the sequence. investigate Cholesky factorization symmetric matrix by using these identities.

We make a first step towards a classification of simple generalized Harish-Chandra modules which are not Harish-Chandra modules or weight modules of finite type. For an arbitrary algebraic reductive pair of complex Lie algebras (g, k), we construct, via cohomological induction, the fundamental series F ·(p, E) of generalized Harish-Chandra modules. We then use F ·(p, E) to characterize any simp...

In this paper, firstly, we define the k-step generalized Balancing sequences and study Binet formula of these sequences. Also, find families super-diagonal matrices such that permanents are elements Finally, examine periods in semi-direct product presented by G = < x, y | x2m−1 y2 1, yxy x−1 > for generating pair (x, y).

‎In this paper we propose a new iteration process‎, ‎called the $K^{ast }$ iteration process‎, ‎for approximation of fixed‎ ‎points‎. ‎We show that our iteration process is faster than the existing well-known iteration processes using numerical examples‎. ‎Stability of the $K^{ast‎}‎$ iteration process is also discussed‎. ‎Finally we prove some weak and strong convergence theorems for Suzuki ge...