Sufficient Conditions For Univalence Obtained By Using Second Order Linear Strong Differential Subordinations,
2010
TÜBİTAK
Sufficient Conditions For Univalence Obtained By Using Second Order Linear Strong Differential Subordinations, Georgia Irina Oros
Turkish Journal of Mathematics
The concept of differential subordination was introduced in [3] by S.S. Miller and P.T. Mocanu and the concept of strong differential subordination was introduced in [1], [2] by J.A. Antonino and S. Romaguera. In [5] we have studied the strong differential subordinations in the general case and in [6] we have studied the first order linear strong differential subordinations. In this paper we study the second order linear strong differential subordinations. Our results may be applied to deduce sufficient conditions for univalence in the unit disc, such as starlikeness, convexity, alpha-convexity, close-to-convexity respectively.
Nontrivial Periodic Solutions Of Nonlinear Functional Differential Systems With Feedback Control,
2010
TÜBİTAK
Nontrivial Periodic Solutions Of Nonlinear Functional Differential Systems With Feedback Control, Yingxin Guo
Turkish Journal of Mathematics
This paper examines the existence of nontrivial periodic solutions for the nonlinear functional differential system with feedback control: \{\aligned x'(t)=x(t)a(t)-\big[\sum_{i=1}^n a_i(t)\int_0^{+\infty} f(t, x(t-\theta)) d}\varphi_i(\theta) +\sum_{j=1}^m b_j(t) \int_0^{+\infty} f(t,x'(t-\theta))\,d}\phi_j(\theta)+\sum_{\mu=1}^p c_\mu(t) \int_0^{\infty} u(t-\theta)\,d}\delta_\mu(\theta)\big], u'(t)=-\rho(t)u(t)+\sum_{\nu=1}^q \beta_\nu(t) \int_0^{\infty} f(t, x(t-\theta))\,d}\psi_\nu(\theta).\endaligned Under certain growth conditions on the nonlinearity f, several sufficient conditions for the existence of nontrivial solution are obtained by using Leray-Schauder nonlinear alternative.
Existence And Uniqueness Of Solutions To Neutral Stochastic Functional Differential Equations With Infinite Delay In L^P(\Omega,C_H), Haibo Bao
Turkish Journal of Mathematics
In this paper, we shall consider the existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay in L^p(\Omega,C_h) space: d[x(t)-G(x_t)]=f(t,x_t)dt+g(t,x_t)dB(t), where we assume f:R^+\times L^p(\Omega,C_h) \to L^p(\Omega,R^n), g:R^+\times L^p(\Omega,C_h) \to L^p(\Omega,L(R^m, R^n)), G: L^p(\Omega,C_h) \to L^p(\Omega,R^n), p>2,\, and B(t) is a given m-dimensional Brownian motion.
On Maximum Principle And Existence Of Positive Weak Solutions For N\Times N Nonlinear Elliptic Systems Involving Degenerated P-Laplacian Operators, H. M. Serag, S. A. Khafagy
Turkish Journal of Mathematics
We study the Maximum Principle and existence of positive weak solutions for the n \times n nonlinear elliptic system -\Delta_{P,p}u_i=\sum_{j=1}^na_{ij}(x) u_j ^{p-2}u_j+f_i(x,u_1,u_2, ... ,u_n) in \Omega, u_i=0,\ i=1,2,. n on \partial \Omega \} where the degenerated p-Laplacian defined as \Delta _{P,p}u=div [P(x) \nabla u ^{p-2}\nabla u] with p>1,p \neq 2 and P(x) is a weight function. We give some conditions for having the Maximum Principle for this system and then we prove the existence of positive weak solutions for the quasilinear system by using ``sub-super solutions method''.
Korovkin Type Approximation Theorem For Functions Of Two Variables In Statistical Sense,
2010
TÜBİTAK
Korovkin Type Approximation Theorem For Functions Of Two Variables In Statistical Sense, Fadi̇me Di̇ri̇k, Kami̇l Demi̇rci̇
Turkish Journal of Mathematics
In this paper, using the concept of A-statistical convergence for double sequences, we investigate a Korovkin-type approximation theorem for sequences of positive linear operator on the space of all continuous real valued functions defined on any compact subset of the real two-dimensional space. Then we display an application which shows that our new result is stronger than its classical version. We also obtain a Voronovskaya-type theorem \ and some differential properties for sequences of positive linear operators constructed by means of the Bernstein polynomials of two variables.
A Note On Dominant Contractions Of Jordan Algebras,
2010
TÜBİTAK
A Note On Dominant Contractions Of Jordan Algebras, Farrukh Mukhamedov, Seyi̇t Temi̇r, Hasan Akin
Turkish Journal of Mathematics
We consider two positive contractions T,S:L_1(A,\tau) \longrightarrow L_1(A,\tau) such that T\leq S, here (A, \tau) is a semi-finite JBW-algebra. If there is an n_0 \in N such that S^{n_0}-T^{n_0}
The Equivalence Of Centro-Equiaffine Curves,
2010
TÜBİTAK
The Equivalence Of Centro-Equiaffine Curves, Yasemi̇n Sağiroğlu, Ömer Pekşen
Turkish Journal of Mathematics
The motivation of this paper is to find formulation of the SL(n,R)-equivalence of curves. The types for centro-equiaffine curves and for every type all invariant parametrizations for such curves are introduced. The problem of SL(n,R)-equivalence of centro-equiaffine curves is reduced to that of paths. The centro-equiaffine curvatures of path as a generating system of the differential ring of SL(n,R)-invariant differential polinomial functions of path are found. Global conditions of SL(n,R)-equivalence of curves are given in terms of the types and invariants. It is proved that the invariants are independent.
A Gap Theorem For Complete Space-Like Hypersurface With Constant Scalar Curvature In Locally Symmetric Lorentz Spaces,
2010
TÜBİTAK
A Gap Theorem For Complete Space-Like Hypersurface With Constant Scalar Curvature In Locally Symmetric Lorentz Spaces, Jiancheng Liu, Lin Wei
Turkish Journal of Mathematics
Let M^n be a complete space-like hypersurface with constant scalar curvature in locally symmetric Lorentz space N^{n+1}_1, S be the squared norm of the second fundamental form of M^n in N^{n+1}_1. In this paper, we obtain a gap property of S: if nP\leq \sup S\leq D(n,P) for some constants P and D(n, P), then either \sup S=nP and M^n is totally umbilical, or \sup S=D(n, P) and M^n has two distinct principal curvatures.
B.-Y. Chen Inequalities For Slant Submanifolds In Quaternionic Space Forms,
2010
TÜBİTAK
B.-Y. Chen Inequalities For Slant Submanifolds In Quaternionic Space Forms, Gabriel Eduard Vilcu
Turkish Journal of Mathematics
In this paper some B.-Y. Chen inequalities for slant submanifolds in quaternionic space forms are established.
Extremal Lagrangian Submanifolds In A Complex Space Form N^N(4c),
2010
TÜBİTAK
Extremal Lagrangian Submanifolds In A Complex Space Form N^N(4c), Shichang Shu, Annie Yi Han
Turkish Journal of Mathematics
Let N^n(4c) be the complex space form of constant holomorphic sectional curvature 4c, \varphi: M \to N^n(4c) be an immersion of an n-dimensional Lagrangian manifold M in N^n(4c). Denote by S and H the square of the length of the second fundamental form and the mean curvature of M. Let \rho be the non-negative function on M defined by \rho^2=S-nH^2, Q be the function which assigns to each point of M the infimum of the Ricci curvature at the point. In this paper, we consider the variational problem for non-negative functional U(\varphi)=\int_M\rho^2dv=\int_M(S-nH^2)dv. We call the critical points of U(\varphi) the …
A Note On The Lyapunov Exponent In Continued Fraction Expansions,
2010
TÜBİTAK
A Note On The Lyapunov Exponent In Continued Fraction Expansions, Jianzhong Cheng, Lu-Ming Shen
Turkish Journal of Mathematics
Let T:[0,1) \to [0,1) be the Gauss transformation. For any irrational x \in [0,1), the Lyapunov exponent \alpha(x) of x is defined as \alpha(x)=\lim_{n\to\infty}\frac{1}{n} \log (T^n)'(x) . By Birkoff Average Theorem, one knows that \alpha(x) exists almost surely. However, in this paper, we will see that the non-typical set \{x\in [0,1):\lim_{n\to\infty}\frac{1}{n} \log (T^n)'(x) does not exist\} carries full Hausdorff dimension.
New Inequalities Similar To Hardy-Hilbert's Inequality,
2010
TÜBİTAK
New Inequalities Similar To Hardy-Hilbert's Inequality, Namita Das, Srinibas Sahoo
Turkish Journal of Mathematics
In this paper, we establish a new inequality similar to Hardy-Hilbert's inequality. As applications, some particular results and the equivalent form are derived. The integral analogues of the main results are also given.
The Riemann Hilbert Problem For Generalized Q-Holomorphic Functions,
2010
TÜBİTAK
The Riemann Hilbert Problem For Generalized Q-Holomorphic Functions, Sezayi̇ Hizliyel, Mehmet Çağliyan
Turkish Journal of Mathematics
In this work, the classical Riemann Hilbert boundary value problem is extended to generalized Q-holomorphic functions.
Trace Formulae For Schrödinger Systems On Graphs,
2010
TÜBİTAK
Trace Formulae For Schrödinger Systems On Graphs, Chuan-Fu Yang, Zhen-You Huang, Xiao-Ping Yang
Turkish Journal of Mathematics
For Schrödinger systems on metric graphs with \delta'-type conditions at the central vertex, firstly, we obtain precise description for the square root of the large eigenvalue up to the o(1/n)-term. Secondly, the regularized trace formulae for Schrödinger systems are calculated with some techniques in classical analysis. Finally, these formulae are used to obtain a result of inverse problem in the spirit of Ambarzumyan.
The Principal Eigencurves For A Nonselfadjoint Elliptic Operator,
2010
TÜBİTAK
The Principal Eigencurves For A Nonselfadjoint Elliptic Operator, Aomar Anane, Omar Chakrone, Abdellah Zerouali
Turkish Journal of Mathematics
In this paper we study the existence of the principal eigencurves for a nonselfadjoint elliptic operator. We obtain their variational formulation. We establish also the continuity and the differentiability of the principal eigencurves.
Structural Properties Of Bilateral Grand Lebesque Spaces,
2010
TÜBİTAK
Structural Properties Of Bilateral Grand Lebesque Spaces, E. Liflyand, E. Ostrovsky, L. Sirota
Turkish Journal of Mathematics
In this paper we study the multiplicative, tensor, Sobolev and convolution inequalities in certain Banach spaces, the so-called Bilateral Grand Lebesque Spaces. We also give examples to show the sharpness of these inequalities when possible.
Direct And Inverse Theorems For The Bézier Variant Of Certain Summation-Integral Type Operators,
2010
TÜBİTAK
Direct And Inverse Theorems For The Bézier Variant Of Certain Summation-Integral Type Operators, Asha Ram Gairola, P. N. Agrawal
Turkish Journal of Mathematics
Recently, the Bézier variant of some well known operators were introduced (cf. [8]-[9]) and their rates of convergence for bounded variation functions have been investigated (cf. [2], [10]). In this paper we establish direct and inverse theorems for the Bézier variant of the operators M_n introduced in [5] in terms of Ditzian-Totik modulus of smoothness \omega_{\varphi^\lambda}(f,t) (0 \leqslant \lambda \leqslant1 ). These operators include the well known Baskakov-Durrmeyer and Szász-Durrmeyer type operators as special cases.
Weak Hardy Space And Endpoint Estimates For Singular Integrals On Space Of Homogeneous Type,
2010
TÜBİTAK
Weak Hardy Space And Endpoint Estimates For Singular Integrals On Space Of Homogeneous Type, Yong Ding, Xinfeng Wu
Turkish Journal of Mathematics
We develop the theory of weak Hardy spaces H^{1,\infty} on space of homogeneous type. As some applications, we show that certain singular integral operators and fractional integral operators are bounded from H^{1,\infty} to L^{1,\infty} and L^{\frac{1}{1-\alpha},\infty}, respectively. We give also the endpoint estimates for Nagel and Stein's singular integrals studied in [10].
On Harmonicity In Some Moufang-Klingenberg Planes,
2010
TÜBİTAK
On Harmonicity In Some Moufang-Klingenberg Planes, Basri̇ Çeli̇k, Ati̇lla Akpinar, Süleyman Çi̇ftçi̇
Turkish Journal of Mathematics
In this paper we study Moufang-Klingenberg planes M (A) defined over a local alternative ring A of dual numbers. We show that some collineations of M (A) preserve cross-ratio and thus establish a relation between harmonicity and harmonic position.
On Purely Real Surfaces In Kaehler Surfaces,
2010
TÜBİTAK
On Purely Real Surfaces In Kaehler Surfaces, Bang-Yen Chen
Turkish Journal of Mathematics
An immersion \phi colon M to \tilde M^2 of a surface M into a Kaehler surface is called purely real if the complex structure J on \tilde M^2 carries the tangent bundle of M into a transversal bundle. In the first part of this article, we prove that the equation of Ricci is a consequence of the equations of Gauss and Codazzi for purely real surfaces in any Kaehler surface. In the second part, we obtain a necessary condition for a purely real surface in a complex space form to be minimal. Several applications of this condition are provided. In …
