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20102 Applied Mathematics
2Fuzzy numbers
2Supporting cone
1Compact sets
1Convergence of a sequence of fuzzy numbers
1Convergence of numerical methods
1Core of a sequence
1Interval maps
1Limit superior and limit inferior
1Natural density
1Non-convex analysis
1Nonconvex optimization
1Nonconvex sets
1Nonlinear differential delay equations
1Number theory
1Optimality conditions
1Singular perturbations
1Statistical boundedness
1Statistical cluster point

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**Authors:**Mammadov, Musa**Date:**2003**Type:**Text , Journal article**Relation:**Abstract and Applied Analysis Vol. 2003, no. 11 (2003), p. 631-650**Full Text:**false**Reviewed:****Description:**We study the turnpike property for the nonconvex optimal control problems described by the differential inclusion x˙∈a(x). We study the infinite horizon problem of maximizing the functional ∫0Tu(x(t))dt as T grows to infinity. The turnpike theorem is proved for the case when a turnpike set consists of several optimal stationary points.**Description:**C1**Description:**2003000343

Global asymptotic stability in a class of nonlinear differential delay equations

- Ivanov, Anatoli, Mammadov, Musa

**Authors:**Ivanov, Anatoli , Mammadov, Musa**Date:**2011**Type:**Text , Journal article**Relation:**Discrete and Continuous Dynamical Systems Vol. 2011, no. Supplement 2011 (2011), p.**Full Text:****Reviewed:****Description:**An essentially nonlinear dierential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are de- rived. An application to a physiological model by M.C. Mackey is treated in detail.**Description:**2003009358

**Authors:**Ivanov, Anatoli , Mammadov, Musa**Date:**2011**Type:**Text , Journal article**Relation:**Discrete and Continuous Dynamical Systems Vol. 2011, no. Supplement 2011 (2011), p.**Full Text:****Reviewed:****Description:**An essentially nonlinear dierential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are de- rived. An application to a physiological model by M.C. Mackey is treated in detail.**Description:**2003009358

Global stability, periodic solutions and optimal control in a nonlinear differential delay model

- Ivanov, Anatoli, Mammadov, Musa

**Authors:**Ivanov, Anatoli , Mammadov, Musa**Date:**2010**Type:**Text , Conference proceedings**Relation:**Eighth Mississippi State - UAB Conference on Differential Equations and Computational Simulations, 2010**Full Text:**false**Description:**A nonlinear differential equation with delay serving as a mathematical model of several applied problmes is considered. Sufficient conditions for the global asymptotic stability and for the existence of periodic solutions are given. Two particular applications are treated in detail. The first one is a blood cell production model by Mackey, for which new periodicity criteria are derived. The second application is a modified economic model with delay due to Ramsay. An optimization problem for a maximal consumption is stated and solved for the latter.

**Authors:**Ivanov, Anatoli , Mammadov, Musa**Date:**2010**Type:**Text , Conference proceedings**Relation:**Eighth Mississippi State - UAB Conference on Differential Equations and Computational Simulations, 2010**Full Text:**false**Description:**A nonlinear differential equation with delay serving as a mathematical model of several applied problmes is considered. Sufficient conditions for the global asymptotic stability and for the existence of periodic solutions are given. Two particular applications are treated in detail. The first one is a blood cell production model by Mackey, for which new periodicity criteria are derived. The second application is a modified economic model with delay due to Ramsay. An optimization problem for a maximal consumption is stated and solved for the latter.

Optimality conditions via weak subdifferentials in reflexive Banach spaces

- Hassani, Sara, Mammadov, Musa, Jamshidi, Mina

**Authors:**Hassani, Sara , Mammadov, Musa , Jamshidi, Mina**Date:**2017**Type:**Text , Journal article**Relation:**Turkish Journal of Mathematics Vol. 41, no. 1 (2017), p. 1-8**Full Text:****Reviewed:****Description:**In this paper the relation between the weak subdifferentials and the directional derivatives, as well as optimality conditions for nonconvex optimization problems in reflexive Banach spaces, are investigated. It partly generalizes several related results obtained for finite dimensional spaces. © Tübitak.

**Authors:**Hassani, Sara , Mammadov, Musa , Jamshidi, Mina**Date:**2017**Type:**Text , Journal article**Relation:**Turkish Journal of Mathematics Vol. 41, no. 1 (2017), p. 1-8**Full Text:****Reviewed:****Description:**In this paper the relation between the weak subdifferentials and the directional derivatives, as well as optimality conditions for nonconvex optimization problems in reflexive Banach spaces, are investigated. It partly generalizes several related results obtained for finite dimensional spaces. © Tübitak.

Sigma supporting cone and optimality conditions in non-convex problems

- Hassani, Sara, Mammadov, Musa

**Authors:**Hassani, Sara , Mammadov, Musa**Date:**2014**Type:**Text , Journal article**Relation:**Far East Journal of Mathematical Sciences Vol. 91, no. 2 (2014), p. 169-190**Full Text:**false**Reviewed:****Description:**In this paper, a new supporting function for characterizing non-convex sets is introduced. The notions of Ïƒ-supporting cone and maximal conic gap are proposed and some properties are investigated. By applying these new notions, we establish the optimality conditions considered in [7] for a broader class of finite dimensional normed spaces in terms of weak subdifferentials.

Statistical cluster points of sequences in finite dimensional spaces

- Pehlivan, Serpil, Guncan, A., Mammadov, Musa

**Authors:**Pehlivan, Serpil , Guncan, A. , Mammadov, Musa**Date:**2004**Type:**Text , Journal article**Relation:**Czechoslovak Mathematical Journal Vol. 54, no. 1 (2004), p. 95-102**Full Text:**false**Reviewed:****Description:**In this paper we study the set of statistical cluster points of sequences in m-dimensional spaces. We show that some properties of the set of statistical cluster points of the real number sequences remain in force for the sequences in m-dimensional spaces too. We also define a notion of T-statistical convergence. A sequence x is**Description:**C1**Description:**2003000896

Statistical limit inferior and limit superior for sequences of fuzzy numbers

- Aytar, Salih, Mammadov, Musa, Pehlivan, Serpil

**Authors:**Aytar, Salih , Mammadov, Musa , Pehlivan, Serpil**Date:**2006**Type:**Text , Journal article**Relation:**Fuzzy Sets and Systems Vol. 157, no. 7 (2006), p. 976-985**Full Text:**false**Reviewed:****Description:**In this paper, we extend the concepts of statistical limit superior and limit inferior (as introduced by Fridy and Orhan [Statistical limit superior and limit inferior, Proc. Amer. Math. Soc. 125 (12) (1997) 3625-3631. [12]]) to statistically bounded sequences of fuzzy numbers and give some fuzzy-analogues of properties of statistical limit superior and limit inferior for sequences of real numbers. © 2005 Elsevier B.V. All rights reserved.**Description:**C1**Description:**2003001832

The core of a sequence of fuzzy numbers

- Aytar, Salih, Pehlivan, Serpil, Mammadov, Musa

**Authors:**Aytar, Salih , Pehlivan, Serpil , Mammadov, Musa**Date:**2008**Type:**Text , Journal article**Relation:**Fuzzy Sets and Systems Vol. 159, no. 24 (2008), p. 3369-3379**Full Text:**false**Reviewed:****Description:**In this paper, based on level sets we define the limit inferior and limit superior of a bounded sequence of fuzzy numbers and prove some properties. We extend the concept of the core of a sequence of complex numbers, first introduced by Knopp in 1930, to a bounded sequence of fuzzy numbers and prove that the core of a sequence of fuzzy numbers is the interval [ν, μ] where ν and μ are extreme limit points of the sequence. © 2008 Elsevier B.V. All rights reserved.

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