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- Fixed point (5)
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Articles 241 - 254 of 254
Full-Text Articles in Physical Sciences and Mathematics
Modified Objective Function Approach For Multitime Variational Problems, Anurag Jayswal, Tadeusz Antczak, Shalini Jha
Modified Objective Function Approach For Multitime Variational Problems, Anurag Jayswal, Tadeusz Antczak, Shalini Jha
Turkish Journal of Mathematics
The present paper is devoted to studying the modified objective function approach used for solving the considered multitime variational problem. In this method, a new multitime variational problem is constructed by modifying the objective function in the original considered multitime variational problem. Further, the equivalence between an optimal solution to the original multitime variational problem and its associated modified problem is established under both hypotheses of invexity and generalized invexity defined for a multitime functional. Thereafter, using the modified objective function method, we derive the saddle-point results for the considered multitime variational problem. Moreover, we provide some examples to illustrate …
On Spacelike Rectifying Slant Helices In Minkowski 3-Space, Bülent Altunkaya, Levent Kula
On Spacelike Rectifying Slant Helices In Minkowski 3-Space, Bülent Altunkaya, Levent Kula
Turkish Journal of Mathematics
In this paper, we study the position vector of a spacelike rectifying slant helix with non-lightlike principal normal vector field in $E_1^3$. First we find the general equations of the curvature and the torsion of spacelike rectifying slant helices. After that, we construct second-order linear differential equations. By their solutions, we determine families of spacelike rectifying slant helices that lie on cones.
Fréchet-Hilbert Spaces And The Property Scbs, Eli̇f Uyanik, Murat Hayretti̇n Yurdakul
Fréchet-Hilbert Spaces And The Property Scbs, Eli̇f Uyanik, Murat Hayretti̇n Yurdakul
Turkish Journal of Mathematics
In this note, we obtain that all separable Fréchet-Hilbert spaces have the property of smallness up to a complemented Banach subspace (SCBS). Djakov, Terzioğlu, Yurdakul, and Zahariuta proved that a bounded perturbation of an automorphism on Fréchet spaces with the SCBS property is stable up to a complemented Banach subspace. Considering Fréchet-Hilbert spaces we show that the bounded perturbation of an automorphism on a separable Fréchet-Hilbert space still takes place up to a complemented Hilbert subspace. Moreover, the strong dual of a real Fréchet-Hilbert space has the SCBS property.
Analysis Of Mixed-Order Caputo Fractional System With Nonlocal Integral Boundary Condition, Tuğba Akman Yildiz, Neda Khodabakhshi, Dumitru Baleanu
Analysis Of Mixed-Order Caputo Fractional System With Nonlocal Integral Boundary Condition, Tuğba Akman Yildiz, Neda Khodabakhshi, Dumitru Baleanu
Turkish Journal of Mathematics
This paper deals with a mixed-order Caputo fractional system with nonlocal integral boundary conditions. This study can be considered as an extension of previous studies, since the orders of the equations lie on different intervals. We discuss the existence and uniqueness of the solution using fixed point methods. We enrich the study with an example.
Conformable Fractional Sturm-Liouville Equation And Some Existenceresults On Time Scales, Tüba Gülşen, Emrah Yilmaz, Hi̇kmet Kemaloğlu
Conformable Fractional Sturm-Liouville Equation And Some Existenceresults On Time Scales, Tüba Gülşen, Emrah Yilmaz, Hi̇kmet Kemaloğlu
Turkish Journal of Mathematics
In this study, we analyze a conformable fractional (CF) Sturm-Liouville (SL) equation with boundary conditions on an arbitrary time scale $\mathbb{T}$. Then we extend the basic spectral properties of the classical SL equation to the CF case. Finally, some sufficient conditions are established to guarantee the existence of a solution for this CF-SL problem on $\mathbb{T}$ by using certain fixed point theorems. For explaining these existence theorems, we give an example with appropriate choices.
On Strongly Autinertial Groups, Cansu Beti̇n Onur
On Strongly Autinertial Groups, Cansu Beti̇n Onur
Turkish Journal of Mathematics
A subgroup $ X $ of $ G $ is said to be inert under automorphisms (autinert) if $ X : X^\alpha \cap X $ is finite for all $ \alpha \in Aut(G)$ and it is called strongly autinert if $ :X $ is finite for all $ \alpha \in Aut(G).$ A group is called strongly autinertial if all subgroups are strongly autinert. In this article, the strongly autinertial groups are studied. We characterize such groups for a finitely generated case. Namely, we prove that a finitely generated group $ G $ is strongly autinertial if and only if one …
A New Class Of Generalized Polynomials, Nabiullah Khan, Talha Usman, Junesang Choi
A New Class Of Generalized Polynomials, Nabiullah Khan, Talha Usman, Junesang Choi
Turkish Journal of Mathematics
Motivated by their importance and potential for applications in a variety of research fields, recently, various polynomials and their extensions have been introduced and investigated. In this sequel, we modify the known generating functions of polynomials, due to both Milne-Thomson and Dere and Simsek, to introduce a new class of generalized polynomials and present some of their involved properties. As obvious special cases of the newly introduced polynomials, we also introduce so-called power sum-Laguerre--Hermite polynomials and generalized Laguerre and Euler polynomials and we present some of their involved identities and formulas. The results presented here, being very general, are pointed …
On The Local Superconvergence Of The Fully Discretized Multiprojection Method For Weakly Singular Volterra Integral Equations Of The Second Kind, Hossein Beyrami, Taher Lotfi
On The Local Superconvergence Of The Fully Discretized Multiprojection Method For Weakly Singular Volterra Integral Equations Of The Second Kind, Hossein Beyrami, Taher Lotfi
Turkish Journal of Mathematics
In this paper, we extend the well-known multiprojection method for solving the second kind of weakly singular Volterra integral equations. We apply this method based on the collocation projection and develop a fully discretized version using appropriate quadrature rules. This method has a superconvergence property that the classic collocation method lacks. Although the new approach results in a significant increase in computational cost, when performing the related matrix-matrix products in parallel the computational time can be reduced. We provide a rigorous mathematical discussion about error analysis of this method. Finally, we present some numerical examples to confirm our theoretical results.
The Brezis-Lieb Lemma In Convergence Vector Lattices, Mohammad Marabeh
The Brezis-Lieb Lemma In Convergence Vector Lattices, Mohammad Marabeh
Turkish Journal of Mathematics
Recently measure-free versions of the Brezis-Lieb lemma were proved for unbounded order convergence in vector lattices. In this article, we extend these versions to convergence vector lattices.
Multiplier And Approximation Theorems In Smirnov Classes Withvariable Exponent, Daniyal Israfilzade, Ahmet Testici
Multiplier And Approximation Theorems In Smirnov Classes Withvariable Exponent, Daniyal Israfilzade, Ahmet Testici
Turkish Journal of Mathematics
Let $G\subset \mathbb{C}$ be a bounded Jordan domain with a rectifiable Dini-smooth boundary $\Gamma $ and let $G^{-}:=ext~ \Gamma $. In terms of the higher order modulus of smoothness the direct and inverse problems of approximation theory in the variable exponent Smirnov classes $E^{p(\cdot )}(G)$ and $E^{p(\cdot )}(G^{-})$ \ are investigated. Moreover, the Marcinkiewicz and Littlewood-Paley type theorems are proved. As a corollary some results on the constructive characterization problems in the generalized Lipschitz classes are presented.
Jakimovski-Leviatan Operators Of Durrmeyer Type Involving Appell Polynomials, Pooja Gupta, Purshottam Narain Agrawal
Jakimovski-Leviatan Operators Of Durrmeyer Type Involving Appell Polynomials, Pooja Gupta, Purshottam Narain Agrawal
Turkish Journal of Mathematics
The purpose of the present paper is to establish the rate of convergence for a Lipschitz-type space and obtain the degree of approximation in terms of Lipschitz-type maximal function for the Durrmeyer type modification of Jakimovski-Leviatan operators based on Appell polynomials. We also study the rate of approximation of these operators in a weighted space of polynomial growth and for functions having a derivative of bounded variation.
On Small Covers Over A Product Of Simplices, Murat Altunbulak, Asli Güçlükan İlhan
On Small Covers Over A Product Of Simplices, Murat Altunbulak, Asli Güçlükan İlhan
Turkish Journal of Mathematics
In this paper, we give a formula for the number of $\mathbb{Z}_2^n$-equivariant homeomorphism classes of small covers over a product of simplices. We also give an upper bound for the number of small covers over a product of simplices up to homeomorphism.
Convergence Analysis And Numerical Solution Of The Benjamin-Bona-Mahony Equation By Lie-Trotter Splitting, Fatma Zürnaci, Nurcan Gücüyenen Kaymak, Muaz Seydaoğlu, Gamze Tanoğlu
Convergence Analysis And Numerical Solution Of The Benjamin-Bona-Mahony Equation By Lie-Trotter Splitting, Fatma Zürnaci, Nurcan Gücüyenen Kaymak, Muaz Seydaoğlu, Gamze Tanoğlu
Turkish Journal of Mathematics
In this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global error estimate is obtained via Lady Windermere's fan argument. Finally, to confirm the expected convergence order, numerical examples are studied.
Generalized Geometry Of Goncharov And Configuration Complexes, Muhammad Khalid, Javed Khan, Azhar Iqbal
Generalized Geometry Of Goncharov And Configuration Complexes, Muhammad Khalid, Javed Khan, Azhar Iqbal
Turkish Journal of Mathematics
In this article, a generalized geometry of Goncharov's complex and the Grassmannian complex will be proposed. First, all new homomorphisms will be defined, and then they will be used extensively to connect the Bloch--Suslin and the Grassmannian complex for weight $n=2$ and then Goncharov's complex with Grassmannian complex for weight $n=3$, up to $n=6$. Lastly, and most importantly, generalized morphisms will be presented to cover the geometry of the Goncharov and Grassmannian complex when weight $n= N$. Associated diagrams will be exhibited, proven to be commutative.