scholarly journals Necessary and sufficient conditions for local Pareto optimality on time scales

2009 ◽  
Vol 161 (6) ◽  
pp. 803-810 ◽  
Author(s):  
A. B. Malinowska ◽  
D. F. M. Torres
Keyword(s):  
Time Scales ◽  
Pareto Optimality ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

On conditions of efficiency of a solution of a multicriteria discrete problem

2002 ◽  
Vol 12 (2) ◽  
Author(s):  
V.A. Emelichev ◽  
A.V. Pashkevich
Keyword(s):  
Wide Class ◽  
Pareto Optimality ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Discrete Problem ◽  
Monotone Functions ◽  
Additive Method ◽  
Finite Set ◽  
Necessary And Sufficient

AbstractFor a wide class of multicriteria (vector) optimisation problems with a finite set of vector constraints, basing on the additive method of aggregating special monotone functions of partial criteria, we obtain necessary and sufficient conditions of efficiency (Pareto-optimality) of a solution.

Fundamental properties of statistical convergence and lacunary statistical convergence on time scales

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4455-4467 ◽  
Author(s):  
Ceylan Turan ◽  
Oktay Duman
Keyword(s):  
Time Scales ◽  
Statistical Convergence ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Tauberian Condition ◽  
Fundamental Properties ◽  
Lacunary Statistical Convergence ◽  
Necessary And Sufficient

In this paper, we first obtain a Tauberian condition for statistical convergence on time scales. We also find necessary and sufficient conditions for the equivalence of statistical convergence and lacunary statistical convergence on time scales. Some significant applications are also presented.

scholarly journals Characterizations of weighted dynamic Hardy-type inequalities with higher-order derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. H. Saker ◽  
R. R. Mahmoud ◽  
K. R. Abdo
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Type Inequality ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Hardy Type Inequality ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Weighted Functions ◽  
Necessary And Sufficient

AbstractIn this paper, we establish some necessary and sufficient conditions for the validity of a generalized dynamic Hardy-type inequality with higher-order derivatives with two different weighted functions on time scales. The corresponding continuous and discrete cases are captured when $\mathbb{T=R}$ T = R and $\mathbb{T=N}$ T = N , respectively. Finally, some applications to our main result are added to conclude some continuous results known in the literature and some other discrete results which are essentially new.

scholarly journals Stability Criteria for Volterra Integrodynamic System

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Nusrat Yasmin ◽  
Awais Younus ◽  
Usman Ali ◽  
Safia Mirza
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Qualitative Behavior ◽  
Lyapunov Functionals ◽  
Stability Criteria ◽  
Necessary And Sufficient

We study conditions under which the solutions of linear Volterra integrodynamic system of the formyΔt=Atyt+∫t0tKt,sysΔsare stable on certain time scales. We construct a number of Lyapunov functionals on time scales from which we obtain necessary and sufficient conditions for stability of Volterra integrodynamic system and also we prove several results concerning qualitative behavior of this system.

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