scholarly journals Fibonacci Sequence and Series by Second Order Difference Operator with Logarithmic Function

10.26524/cm39 ◽  
2018 ◽  
Vol 2 (2) ◽  
pp. 51-60
Author(s):  
Rajiniganth P ◽  
Britto Antony Xavier G
Keyword(s):  
Difference Operator ◽  
Fibonacci Sequence ◽  
Second Order ◽  
Logarithmic Function ◽  
Order Difference

scholarly journals Fibonacci Sequence and its Sum by Second Order Difference Operator with Polynomial Factorial

10.26524/cm36 ◽  
2018 ◽  
Vol 2 (2) ◽  
pp. 20-29
Author(s):  
Sandra Pinelas ◽  
Rajiniganth P
Keyword(s):  
Difference Operator ◽  
Fibonacci Sequence ◽  
Second Order ◽  
Order Difference

scholarly journals Advanced fibonacci sequence and its sum by second order variable co-efficient difference operator

2021 ◽  
Vol 5 (2) ◽  
pp. 92-101
Author(s):  
Rajiniganth P ◽  
Britto Antony Xavier G
Keyword(s):  
Difference Operator ◽  
Fibonacci Sequence ◽  
Second Order ◽  
Order Difference ◽  
Order Variable

We introduce a second order difference operator with specific powers of variable co-efficient and its inverse in this study, which allows us to derive the (α1tr1, α2tr2 )-Fibonacci sequence and its summation. This series is known as the Fibonacci sequence with variable co-efficients (VCFS). On the sum of the terms of the variable co-efficient Fibonacci sequence, some theorems and intriguing findings are generated. To demonstrate our findings, appropriate instances arepresented.

scholarly journals Spectrum of Discrete Second-Order Difference Operator with Sign-Changing Weight and Its Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Ruyun Ma ◽  
Chenghua Gao
Keyword(s):  
Eigenvalue Problems ◽  
Difference Operator ◽  
Second Order ◽  
Order Difference ◽  
Sign Changing Solutions

LetT>1be an integer, and let𝕋=1,2,…,T. We discuss the spectrum of discrete linear second-order eigenvalue problemsΔ2ut-1+λmtut=0, t∈𝕋,  u0=uT+1=0, whereλ≠0is a parameter,m:𝕋→ℝchanges sign andmt≠0on𝕋. At last, as an application of this spectrum result, we show the existence of sign-changing solutions of discrete nonlinear second-order problems by using bifurcate technique.

Spectral properties of a nonlocal second-order difference operator

2014 ◽  
Vol 50 (7) ◽  
pp. 938-946
Author(s):  
A. Yu. Mokin
Keyword(s):  
Spectral Properties ◽  
Difference Operator ◽  
Second Order ◽  
Order Difference

Non-self-adjoint difference operators and their spectrum

2005 ◽  
Vol 461 (2057) ◽  
pp. 1505-1531 ◽  
Author(s):  
Robert Howard Wilson
Keyword(s):  
Difference Operator ◽  
Discrete Analogue ◽  
Second Order ◽  
Difference Operators ◽  
Essential Difference ◽  
Order Difference ◽  
Second Order Differential Equations ◽  
Forward Difference ◽  
Difference Expression ◽  
Complex Coefficients

Initially, this paper is a discrete analogue of the work of Brown et al. (1999 Proc. R. Soc. A 455 , 1235–1257) on second-order differential equations with complex coefficients. That is, we investigate the general non-self-adjoint second-order difference expression where the coefficients p n and q n are complex and Δ is the forward difference operator, i.e. Δ x n = x n +1 − x n . Properties of the so-called Hellinger–Nevanlinna m -function for the recurrence relation Mx n = λ w n x n , where the w n are real and positive, are examined, and relationships between the properties of the m -function and the spectrum of the associated operator are explored. However, an essential difference between the continuous and the discrete case arises in the way in which we define the operator natural to the problem. Nevertheless, analogous results regarding the spectrum of this operator are obtained.

scholarly journals On the fine spectrum of the second order difference operator over the sequence spaces ℓp and bvp,(1<p<∞)

2012 ◽  
Vol 55 (3-4) ◽  
pp. 426-431 ◽  
Author(s):  
Vatan Karakaya ◽  
Manaf Dzh. Manafov ◽  
Necip Şi̇mşek
Keyword(s):  
Difference Operator ◽  
Second Order ◽  
Sequence Spaces ◽  
Order Difference ◽  
Fine Spectrum

DISCRETENESS OF THE SPECTRUM OF A NONSELFADJOINT SECOND-ORDER DIFFERENCE OPERATOR

2009 ◽  
Author(s):  
EBRU ERGÜN ◽  
GUSEIN S. GUSEINOV
Keyword(s):  
Difference Operator ◽  
Second Order ◽  
Order Difference
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