# Search results

Mathematical Methods in the Applied Sciences > 44 > 9 > 7442 - 7454

Mathematical Methods in the Applied Sciences > 44 > 6 > 4607 - 4615

Mathematical Methods in the Applied Sciences > 42 > 16 > 5535 - 5550

*x*

^{2}=

*k*

*x*+ 1 for

*k*is any positive integer which is the characteristic equation of the recurrence relation of

*k*‐Fibonacci (

*k*‐Lucas) numbers. This paper is about the metallic ratio in ${Z}_{p}$. We define

*k*‐Fibonacci and

*k*‐Lucas numbers in ${Z}_{p}$, and we show that metallic ratio can be calculated in ${Z}_{p}$ if and only if

*p*≡ ± 1 mod (

*k*

^{2}+ 4), which is...

Mathematical Methods in the Applied Sciences > 42 > 16 > 5143 - 5153

*T*:

*X*→

*Y*is the best possible value of

*U*satisfying the inequality and lower bound for

*T*is the value of

*L*satisfying the inequality where ‖.‖

_{X}and ‖.‖

_{Y}are the norms on the spaces

*X*and

*Y*, respectively. The main goal of this paper is to compute norms and lower bounds for some matrix operators from the weighted sequence space

*ℓ*

_{p}(

*w*) into a new space called as Fibonacci weighted difference...

Astrophysics and Space Science > 2019 > 364 > 9 > 1-15

Iranian Journal of Science and Technology, Transactions A: Science > 2019 > 43 > 6 > 2871-2877

Journal of Inequalities and Applications > 2019 > 2019 > 1 > 1-7

*F̂*and ideal convergence defined the notion of c0I(Fˆ) $c_{0}^{I}(\hat{F})$, cI(Fˆ) $c^{I}(\hat{F})$ and l∞I(Fˆ) $l_{\infty }^{I}(\hat{F})$. In this paper, we give the ideal convergence of Fibonacci...

Journal of Inequalities and Applications > 2019 > 2019 > 1 > 1-5

*E*in the sequence space ℓp (1≤p<∞) $(1\le p<\infty )$. In this paper, we consider the transpose of Nörlund matrix associated with a nonnegative and nonincreasing sequence as an operator mapping ℓp into the...

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 2 > 367-384

*a*

_{1},

*a*

_{2}, …,

*a*

_{m}} of positive integers is called a Diophantine

*m*-tuple if

*a*

_{i}

*a*

_{j}+ 1 is a perfect square for all 1 ≤

*i*<

*j*≤

*m*. In this paper, we prove that if {

*F*

_{2k},

*F*

_{2k+4},

*c*} is a Diophantine triple then there is a unique positive integer

*d*such that

*c < d*and {

*F*

_{2k},

*F*

_{2k+4},

*c, d*} is a Diophantine quadruple.

Decisions in Economics and Finance > 2018 > 41 > 2 > 489-529

The Journal of Analysis > 2019 > 27 > 3 > 761-779

Multimedia Tools and Applications > 2018 > 77 > 19 > 25607- 25627

Discussiones Mathematicae Graph Theory > 2017 > 38 > 1 > 121-133

Chaos, Solitons & Fractals > 2018 > 106 > C > 67-71

Journal of Mathematics and Applications > 2018 > Vol. 41 > 195--206

Chaos, Solitons & Fractals > 2017 > 105 > C > 208-214

IEEE Transactions on Information Theory > 2017 > 63 > 10 > 6530 - 6537

Journal of Inequalities and Applications > 2017 > 2017 > 1 > 1-15

Periodica Mathematica Hungarica > 2017 > 75 > 2 > 221-243

*t*-metric Mahler measure, denoted $$m_t(\alpha )$$ m t ...