scholarly journals Tauberian conditions with controlled oscillatory behavior

2012 ◽  
Vol 25 (3) ◽  
pp. 252-256 ◽  
Author(s):  
İbrahim Çanak ◽  
Ümit Totur ◽  
Bilender P. Allahverdiev
Keyword(s):  
Oscillatory Behavior ◽  
Tauberian Conditions

Some Tauberian conditions for Cesàro summability method

2012 ◽  
Vol 62 (2) ◽  
Author(s):  
İbrahi̇m Çanak ◽  
Ümi̇t Totur
Keyword(s):  
Finite Number ◽  
Oscillatory Behavior ◽  
Summability Method ◽  
Tauberian Theorems ◽  
Integer Part ◽  
Real Numbers ◽  
General Control ◽  
Integer Order ◽  
Tauberian Conditions ◽  
General Control Modulo

AbstractLet u = (u n) be a sequence of real numbers whose generator sequence is Cesàro summable to a finite number. We prove that (u n) is slowly oscillating if the sequence of Cesàro means of (ω n(m−1)(u)) is increasing and the following two conditions are hold: $$\begin{gathered} \left( {\lambda - 1} \right)\mathop {\lim \sup }\limits_n \left( {\frac{1} {{\left[ {\lambda n} \right] - n}}\sum\limits_{k = n + 1}^{\left[ {\lambda n} \right]} {\left( {\omega _k^{\left( m \right)} \left( u \right)} \right)^q } } \right)^{\frac{1} {q}} = o\left( 1 \right), \lambda \to 1^ + , q > 1, \hfill \\ \left( {1 - \lambda } \right)\mathop {\lim \sup }\limits_n \left( {\frac{1} {{n - \left[ {\lambda n} \right]}}\sum\limits_{k = \left[ {\lambda n} \right] + 1}^n {\left( {\omega _k^{\left( m \right)} \left( u \right)} \right)^q } } \right)^{\frac{1} {q}} = o\left( 1 \right), \lambda \to 1^ - , q > 1, \hfill \\ \end{gathered}$$ where (ω n(m) (u)) is the general control modulo of the oscillatory behavior of integer order m ≥ 1 of a sequence (u n) defined in [DİK, F.: Tauberian theorems for convergence and subsequential convergence with moderately oscillatory behavior, Math. Morav. 5, (2001), 19–56] and [λn] denotes the integer part of λn.

scholarly journals Tauberian conditions for a general limitable method

2006 ◽  
Vol 2006 ◽  
pp. 1-6
Author(s):  
İbrahim Canak ◽  
Ümit Totur
Keyword(s):  
Oscillatory Behavior ◽  
Real Numbers ◽  
General Control ◽  
Tauberian Condition ◽  
Integer Order ◽  
Tauberian Conditions ◽  
General Control Modulo ◽  
Classical Control

Let(un)be a sequence of real numbers,Lan additive limitable method with some property, andanddifferent spaces of sequences related to each other. We prove that if the classical control modulo of the oscillatory behavior of(un)inis a Tauberian condition forL, then the general control modulo of the oscillatory behavior of integer ordermof(un)inoris also a Tauberian condition forL.

scholarly journals Tauberian conditions with controlled oscillatory behavior for statistical convergence

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3853-3865
Author(s):  
Sefa Sezer ◽  
Rahmet Savaş ◽  
İbrahim Çanak
Keyword(s):  
Finite Number ◽  
Statistical Convergence ◽  
Oscillatory Behavior ◽  
Summability Method ◽  
Tauberian Theorems ◽  
Real Sequence ◽  
Tauberian Conditions

We present new Tauberian conditions in terms of the general logarithmic control modulo of the oscillatory behavior of a real sequence (sn) to obtain lim n?? sn = ? from st - lim n?? sn = ?, where ? is a finite number. We also introduce the statistical (l,m) summability method and extend some Tauberian theorems to this method. The main results improve some well-known Tauberian theorems obtained for the statistical convergence.

Thermoelectric properties of B12N12 molecule

2019 ◽  
Vol 16 ◽  
Author(s):  
Mohammad Reza Niazian ◽  
Laleh Farhang Matin ◽  
Mojtaba Yaghobi ◽  
Amir Ali Masoudi
Keyword(s):  
Molecular Electronics ◽  
Thermoelectric Properties ◽  
Electronic Devices ◽  
Thermal Conductance ◽  
Wide Band ◽  
Oscillatory Behavior ◽  
Mapping Technique ◽  
Junction Points ◽  
Inelastic Behaviour ◽  
New Generation

Background: Recently, molecular electronics have attracted the attention of many researchers, both theoretically and applied electronics.Nanostructures have significant thermal properties, which is why they are considered as good options for designing a new generation of integrated electronic devices. Objective: In this paper, the focus is on the thermoelectric properties of the molecular junction points with the electrodes. Also, the influence of the number of atom contacts was investigated on the thermoelectric properties of molecule located between two electrodes metallic.Therefore, the thermoelectric characteristics of the B12 N12 molecule are investigated. Methods: For this purpose, the Green’s function theory as well as mapping technique approach with the wide-band approximation and also the inelastic behaviour is considered for the electron-phonon interactions. Results & Conclusion: Results & Conclusion:It is observed that the largest values of the total part of conductance as well as its elastic (G(e,n)max) depends on the number of atom contacts and are arranged as: G(e,1)max>G(e,4)max>G(e,6)max. Furthermore, the largest values of the electronic thermal conductance, i.e. Kpmax is seen to be in the order of K(p,4)max < K(p,1)max < K(p,6)max that the number of main peaks increases in four-atom contacts at (E<Ef). Furthermore, it is represented that the thermal conductance shows an oscillatory behavior which is significantly affected by the number of atom contacts.

scholarly journals Oscillatory behavior of nonlinear Hilfer fractional difference equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tuğba Yalçın Uzun
Keyword(s):  
Difference Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Oscillatory Behavior ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
All Solutions ◽  
Alpha Beta

AbstractIn this paper, we study the oscillation behavior for higher order nonlinear Hilfer fractional difference equations of the type $$\begin{aligned}& \Delta _{a}^{\alpha ,\beta }y(x)+f_{1} \bigl(x,y(x+\alpha ) \bigr) =\omega (x)+f_{2} \bigl(x,y(x+ \alpha ) \bigr),\quad x\in \mathbb{N}_{a+n-\alpha }, \\& \Delta _{a}^{k-(n-\gamma )}y(x) \big|_{x=a+n-\gamma } = y_{k}, \quad k= 0,1,\ldots,n, \end{aligned}$$ Δ a α , β y ( x ) + f 1 ( x , y ( x + α ) ) = ω ( x ) + f 2 ( x , y ( x + α ) ) , x ∈ N a + n − α , Δ a k − ( n − γ ) y ( x ) | x = a + n − γ = y k , k = 0 , 1 , … , n , where $\lceil \alpha \rceil =n$ ⌈ α ⌉ = n , $n\in \mathbb{N}_{0}$ n ∈ N 0 and $0\leq \beta \leq 1$ 0 ≤ β ≤ 1 . We introduce some sufficient conditions for all solutions and give an illustrative example for our results.

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