Generalized multivariate Fink-type identity and some related results on time scales with applications

2019 ◽  
Vol 25 (2) ◽  
pp. 189-203
Author(s):  
Sabir Hussain ◽  
Muhammad Amer Latif
Keyword(s):  
Time Scales ◽  
Discrete Version ◽  
Generalized Polynomials ◽  
Arbitrary Time ◽  
Type Identity ◽  
Grüss Type Inequalities ◽  
New Applications

Abstract Generalized Fink-type identity for multi-variables to an arbitrary time scales is obtained, giving some multi-variate Ostrowski, Iyengar and Grüss-type inequalities unifying the corresponding continuous and discrete version. Some new applications to generalized polynomials are also obtained.

scholarly journals Some inequalities of Ostrowski and Grüss type for triple integrals on time scales

2011 ◽  
Vol 42 (4) ◽  
pp. 415-426 ◽  
Author(s):  
Nazir Ahmad Mir ◽  
Roman Ullah
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Partial Derivatives ◽  
Arbitrary Time ◽  
Grüss Type Inequalities

In this paper, we establish some inequalities of Ostrowski and Grüss type for triple integrals on arbitrary time scales involving three functions and their partial derivatives. We also discuss the discrete Ostrowski and Grüss type inequalities for triple sumon time scale.

scholarly journals Generalized Weighted Ostrowski, Trapezoid and Grüss Type Inequalities on Time Scales

2018 ◽  
Vol 60 (1) ◽  
pp. 123-144 ◽  
Author(s):  
A. A. El-Deeb ◽  
H. A. Elsennary ◽  
Eze R. Nwaeze
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Type Inequality ◽  
Quantum Calculus ◽  
Arbitrary Time ◽  
Ostrowski Type Inequality ◽  
Grüss Type Inequalities ◽  
Two Parameters ◽  
Delta Derivatives

Abstract In this article, using two parameters, we obtain generalizations of a weighted Ostrowski type inequality and its companion inequalities on an arbitrary time scale for functions whose first delta derivatives are bounded. Our work unifies the continuous and discrete versions and can also be applied to the quantum calculus case.

scholarly journals On weighted Čebyšev-Grüss type inequalities on time scales

2008 ◽  
pp. 185-195 ◽  
Author(s):  
Mehmet Zeki Sarikaya ◽  
Nesip Aktan ◽  
Hüseyin Yildirim
Keyword(s):  
Time Scales ◽  
Grüss Type Inequalities

scholarly journals Turbulent Intermittency in a Random Fiber Laser

Atoms ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 43 ◽  
Author(s):  
Antônio Macêdo ◽  
Iván González ◽  
Ernesto Raposo ◽  
Leonardo Menezes ◽  
Anderson Gomes
Keyword(s):  
Fiber Laser ◽  
Time Scales ◽  
Continuous Wave ◽  
Discrete Version ◽  
Fluid Turbulence ◽  
Turbulence Intermittency ◽  
Direct Interpretation ◽  
Heavy Tailed ◽  
Non Gaussian ◽  
Short Time

In fluid turbulence, intermittency is the emergence of non-Gaussian tails in the distribution of velocity increments in small space and/or time scales. Intermittence is thus expected to gradually disappear as one moves from small to large scales. Here we study the turbulent-like intermittency effect experimentally observed in the distribution of intensity fluctuations in a disordered continuous-wave-pumped erbium-doped-based random fiber laser with specially-designed random fiber Bragg gratings. The intermittency effect is investigated as a crossover in the distribution of intensity increments from a heavy-tailed distribution (for short time scales), to a Gaussian distribution (for large time scales). The results are theoretically supported by a hierarchical stochastic model that incorporates Kolmogorov’s theory of turbulence. In particular, the discrete version of the hierachical model allows a general direct interpretation of the number of relevant scales in the photonic hierarchy as the order of the transitions induced by the non-linearities in the medium. Our results thus provide further statistical evidence for the interpretation of the turbulence-like emission previously observed in this system.

Oscillation criteria for higher order nonlinear delay dynamic equations on time scales

2016 ◽  
Vol 66 (3) ◽  
Author(s):  
Xin Wu ◽  
Taixiang Sun
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Time Scale ◽  
Higher Order ◽  
Dynamic Equations ◽  
Oscillation Criteria ◽  
Arbitrary Time ◽  
Delay Dynamic Equation ◽  
Delay Dynamic Equations ◽  
Nonlinear Delay

AbstractIn this paper, we study the oscillation criteria of the following higher order nonlinear delay dynamic equationon an arbitrary time scalewith

scholarly journals Lyapunov-Type Inequalities for Some Quasilinear Dynamic System Involving the(p1,p2,…,pm)-Laplacian on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Xiaofei He ◽  
Qi-Ming Zhang
Keyword(s):  
Dynamic System ◽  
Time Scales ◽  
Time Scale ◽  
Arbitrary Time

We establish several new Lyapunov-type inequalities for some quasilinear dynamic system involving the(p1,p2,…,pm)-Laplacian on an arbitrary time scale𝕋, which generalize and improve some related existing results including the continuous and discrete cases.

Sign in / Sign up

Export Citation Format

Share Document