Yucel Turker Ulutas

Parametrized Fibonacci search method with k-Lucas numbers

Abstract In this paper, we study on Fibonacci search method with k -Lucas numbers by introducing a parameter α which depends on the length of the interval and the function. This parameter ensures that the result we got at the end of the computation is correct. We made more improvement in algorithm which finds the maximum point of a unimodal function. Application of this algorithm gives better results.

Two Variants of the Reciprocal Super Catalan Matrix

In this paper, we define two kinds variants of the super Catalan matrix as well as their q-analoques. We give explicit expressions for LU-decompositions of these matrices and their inverses.

Generalized Binomial Convolution of the mth Powers of the Consecutive Integers with the General Fibonacci Sequence

Abstract In this paper, we consider Gauthier’s generalized convolution and then define its binomial analogue as well as alternating binomial analogue. We formulate these convolutions and give some applications of them.

A curious matrix-sum identity and certain finite sums identities

In this paper, we consider two generalized binary sequences and then give a generalization of a matrix equality proposed as an advanced problem. Then, we derive new certain finite sums including the generalized binary sequences as applications.

Some Finite Sums Involving Generalized Fibonacci and Lucas Numbers

By considering Melhams sums (Melham, 2004), we compute various more general nonalternating sums, alternating sums, and sums that alternate according to (−1)2𝑛

Optimization by k-Lucas numbers

This article presents a mathematical analysis of Fibonacci search method by k-Lucas numbers. In this study, we develop a new algorithm which determines the maximum point of unimodal functions on closed intervals. As a result, it makes Fibonacci search method more effective.