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Öğe A generalization of interval-valued optimization problems and optimality conditions by using scalarization and subdifferentials(Academic Publication Council, 2021) Karaman, EmrahIn this work, interval-valued optimization problems are considered. The ordering cone is used to generalize the interval-valued optimization problems on real topological vector spaces. Some definitions and their properties are obtained for intervals, defined via an ordering cone. Gerstewitz's function is used to derive scalarization for the interval-valued optimization problems. Also, two subdifferentials for interval-valued functions are introduced by using subgradients. Some necessary optimality conditions are obtained via subdifferentials and scalarization. An example is given to demonstrate the results.Öğe Gömme fonksiyonu kullanılarak küme optimizasyonuna göre verilen küme değerli optimizasyon problemlerinin optimallik koşulları(2019) Karaman, EmrahBu çalışmada küme değerli optimizasyon problemi ele alınmıştır. Küme değerli optimizasyon problemlerinin çözümlerini bulmak için kullanılan bazı kriterler vardır. Literatürde en çok kullanılan kriterler küme yaklaşımı ve vektör yaklaşımıdır. Bu çalışmada ise küme değerli optimizasyon problemlerinin küme yaklaşımına göre çözümleri araştırıldı. Küme değerli optimizasyon problemlerinin küme yaklaşımına göre optimallik koşullarını elde etmek için skalerizasyon, vektörizasyon ve yönlü türev gibi yöntemler kullanılır. Bu yöntemlerden farklı olarak çalışmada problemin optimallik koşullarını elde etmek için gömme fonksiyonu kullanılmıştır. Gömme fonksiyonu ile optimallik koşullarını elde edebilmek için bir gömme uzayı kullanılmıştır. Bu uzayın ve gömme fonksiyonunun bazı özellikleri incelenmiştir. Bunlara ek olarak çalışmanın daha iyi anlaşılabilmesi için bir örnek verilmiştir.Öğe Optimality Conditions in Set-valued Optimization Problem with Respect to a Partial Order Relation via Directional Derivative(Mathematical Soc Rep China, 2020) Karaman, Emrah; Soyertem, Mustafa; Guvenc, Ilknur AtaseverIn this study, a new directional derivative is defined by using Minkowski difference. Some properties and existence theorems of this directional derivative are given. Moreover, necessary and sufficient optimality conditions are presented for set-valued optimization problems with respect to m(1) order relation via directional derivative.Öğe Optimality conditions in set-valued optimization problems with respect to a partial order relation by using subdifferentials(Taylor & Francis Ltd, 2021) Karaman, Emrah; Guvenc, Ilknur Atasever; Soyertem, MustafaIn this study, set-valued optimization problems are considered with respect to -order relation, which is a partial order relation on the family of nonempty and bounded sets. Four subdifferentials are defined for set-valued optimization maps. Some existence theorems and relations among these subdifferentials are obtained. By using them, necessary and sufficient optimality conditions are presented for set-valued optimization problems with respect to -order relation.Öğe Optimality Conditions of Interval-Valued Optimization Problems by Using Subdifferentials(Gazi Univ, 2020) Karaman, EmrahIn this study, interval-valued optimization problems (shortly, interval optimization) are considered. In order to obtain optimality conditions of interval optimization, subdifferential and weak subdifferential are defined. After some properties including an existence condition of the subdifferentials are studied, optimality conditions including the necessary and sufficient conditions for interval optimization are obtained.Öğe Oscillation and Asymptotic Behaviour of a Higher-Order Nonlinear Neutral-Type Functional Differential Equation with Oscillating Coefficients(Hindawi Publishing Corporation, 2011) Yildiz, Mustafa Kemal; Karaman, Emrah; Durur, HulyaWe will study oscillation of bounded solutions of higher-order nonlinear neutral delay differential equations of the following type: [y(t) + p(t)f(y)(tau(t)))]((n)) + q(t)h(y(sigma(t))) = 0, t >= t(0), t is an element of R, where p is an element of C([t(0),infinity),R), lim(t) (->) (infinity)p(t) = 0, q is an element of C([t(0),infinity), R(+)), tau(t), sigma(t) is an element of C([t(0), infinity),R), tau(t), sigma(t) < t, lim(t) (->) (infinity)tau(t), sigma(t) = infinity, and f, h is an element of C(R, R). We obtain sufficient conditions for the oscillation of all solutions of this equation.Öğe Oscillatory Behavior Of A Higher-Order Nonlinear Neutral Type Functional Difference Equation With Oscillating Coefficients(Tsing Hua Univ, Dept Mathematics, 2014) Karaman, Emrah; Yildiz, Mustafa KemalIn this work, we shall consider oscillation of bounded solutions of higher-order nonlinear neutral delay difference equations of the following type Delta(n)[y (t) + p (t) f (y(tau(t)))] + q (t) h (y (sigma (t))) = 0,t is an element of N, where n is an element of{2,3,...} is fixed and can take both odd and even values, {p(t)}(t=1)(infinity) is a sequence of reals such that lim(t ->infinity) p(t) = 0, {q(t)}(t=1)(infinity) is a nonnegative sequence of reals, and {tau(t)}(t=1)(infinity) and {sigma(t)}(t=1)(infinity) are sequences of integers tending to infinity asymptotically and bounded above by {t}(t=1)(infinity), and f, h is an element of C(R,R).Öğe Some Optimality Criteria of Interval Programming Problems(Springernature, 2021) Karaman, EmrahIn this work, interval programming problems are considered for financial investment and optimality criteria. An order relation, defined by Ishibuchi and Tanaka for maximization problems, is used to obtain the solution of the problems. A real-life example, related to investment, and its solution are given. Necessary and sufficient optimality criteria including weak and strongly solution for interval programming problems are introduced via basic calculus rule, scalarization, and vectorization.
