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In this paper, two kinds of system of fuzzy differential inclusions are introduced and studied. An existence of the solutions for one system of fuzzy differential inclusions is proved by using continuous selection theorem. An existence of the solutions for another system of fuzzy differential inclusions is also proved by employing the fixed point theorem in the generalized metric space. The results presented in this paper improve and extend some known results concerned with the multivalued Cauchy problem and fuzzy differential inclusions.

In this paper, we study the symmetric generalized quasi-variational inclusion problems. Then, we establish some existence theorems of solution sets for these problems. Moreover, the stability of solutions for these problems are also onbtained. Finally, we apply these results to symmetric vector quasi-equilibrium problems. The results presented in this paper improve and extend the main results in the literature. Some examples are given to illustrate our results.

The objective of this paper is to systematically investigate the dynamical properties of a ratio-dependent predator-prey system with Holling type IV functional response by white noise. The global existence of a positive unique solution to the system with positive initial value is shown employing comparison theorem of stochastic equation and It^o's formula. We derived some appropriate conditions for the persistence in mean and extinction. This system has a stable stationary distribution and it is ergodic. Numerical simulations are carried out for further support of present research.

Solving linear systems is a classical problem of engineering and numerical analysis which has various applications in many sciences and engineering. In this paper, we study efficient iterative methods, based on the diagonal and off-diagonal splitting of the coefficient matrix A for solving linear system Ax = b, where A ? Cnxn is nonsingular and x,b ? Cnxm. The new method is a two-parameter two-step method that has some iterative methods as its special cases. Numerical examples are presented to illustrate the effectiveness of the new method.

In this paper, the generalized orthogonal solutions to the matrix inverse problem $AX=B$ and associated optimal approximation problem are considered. The properties and structure of generalized orthogonal matrices are given, the relationships between the generalized orthogonal matrices and the orthogonal matrices are discussed. Necessary and sufficient conditions that the matrix inverse problem $AX=B$ is solvable, the general expression of solution, and it's procrustes problem are discussed. Moreover, the corresponding optimal approximation solutions are given. Finally, we give the algorithms and corresponding computational examples.

In this paper, we determine the coefficient bounds for functions in certain subclasses of close-to-convex functions of complex order, which are introduced here by means of a certain non-homogeneous Cauchy-Euler-type differential equation of order m. Relevant connections of some of the results obtained with those in earlier works are also provided.

In this paper, we study the existence and uniqueness theorem for Lp (1 < p < 2) solutions to a class of infinite time interval backward doubly stochastic differential equations (BDSDEs). Furthermore, we obtain the comparison theorem for 1-dimensional infinite time interval BDSDEs in Lp.

In this paper we study the global dynamics of stochastic predator-prey models with non constant mortality rate and Holling type II response. Concretely, we establish sufficient conditions for the extinction and persistence in the mean of autonomous stochastic model and obtain a critical value between them. Then by constructing appropriate Lyapunov functions, we prove that there is a nontrivial positive periodic solution to the non-autonomous stochastic model. Finally, numerical examples are introduced to illustrate the results developed.

In this paper we introduce a new algorithm based on viscosity approximation method for solving the generalized multiple-set split feasibility problem (GMSSFP)in an infinite dimensional Hilbert spaces . We establish the strong convergence for the algorithm to find a unique solution of the variational inequality which is the optimality condition for the minimization problem.

The aim of this paper is to establish a new version of Ostrowski's type integral inequality. The results are obtained by using a new type of kernel with five sections which improves the approximation errors. Applications to a composite quadrature rule and to Cumulative Distributive Functions are considered

In this paper, we give a generalization of the integral type Jakimovski-Leviatan operators, introduced by Ciupa [1]. Theorems on convergence and the rate of convergence of the operators by using the first and second order modulus of continuity are established. We also study the convergence of these operators in a weighted space of functions.

In this paper, we consider a class of nonsmooth minimax programming problems in which functions are locally Lipschitz. Sucient optimality conditions are discussed under locally Lipschitz generalized (?,?)-invex functions. Moreover, usual duality results are proved under the said assumptions.

In this paper we provide existence and uniqueness results for linear operator equations of the form (I+Am) x = f , where A is a self-adjoint operator in Hilbert space. Some applications to the study of invertible matrices are also presented.

In this paper, fixed point and variational inclusion problems are investigated based on a proximal-type iterative algorithm. Strong convergence theorems are established in the framework of Hilbert spaces.

The purpose of this paper is to investigate variational inequalities, fixed point problems and generalized mixed equilibrium problems. Anextragradient iterative algorithm is investigated in the framework of Hilbert spaces. Weak convergence theorems for common solutions are established.

In this paper, we establish some theorems on approximation and Voronovskaja type results for complex modified Sz?sz-Mirakjan-Stancu operators attached to analytic functions having exponential growth on compact disks. Also, we estimate the rate of convergence and the exact order of approximation.

In this paper we obtain the general solution of a mixed additive and quartic functional equation. We also prove the Hyers-Ulam stability of this functional equation in random normed spaces.

In the present paper, we investigate approximation of analytic functions and their derivatives in a bounded simply connected domain by the sequences of linear operators without the properties of k?positivity.

In this paper, we address a Cauchy problem for elliptic equations with inhomoge- neous source data. The problem is shown to be ill-posed as the solution exhibits an unstable dependence on the given data functions. Here, we shall deal with this problem by using two di erent regularized methods. Moreover, convergence estimates are established under some priori assumptions on the exact solution. Some numerical examples are given to illuminate the e ect of our methods. Keywords and phrases: Cauchy problem; Ill-posed problem; Convergence estimates. Mathematics subject Classification 2000: 35K05, 35K99, 47J06, 47H10

In this paper, we prove the Hyers-Ulam stability of the following generalized additive functional equation ?1? i < j ? m f(xi+xj/2 + m-2?l=1,kl?i,j) = (m-1)2/2 m?i=1 f(xi) where m is a positive integer greater than 3, in various normed spaces.

In this paper, we study a nondifferentiable minimax fractional programming problem under the assumptions of generalized second order (F , α, ρ,d)−convexity. A second order parametric dual is formulated. Weak, strong and converse duality theorems are established in order to relate the primal and dual problems under the afore-said assumptions.

This paper is concerned with the relative controllability for a class of dynamical control systems described by semilinear fractional stochastic dierential equations with nonlocal conditions in Hilbert space. Sucient conditions for relative controllability results are obtained using Schaefer's xed point theorem. An example is provided to show the application of our result

The Sylvester equation has numerous applications in control and system theory, power system, linear algebra, model reduction and signal processing. In the present paper, a global transpose-free quasi- minimal residual method for the Sylvester equations is proposed. The resulting method, with short- term recurrences, does not involve the multiplication with the transpose of the coefficient matrices, and often exhibits smoother convergence behavior than some other existing global methods. Finally, several numerical examples are reported by comparing the proposed method with some global methods.

In this paper, we consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi for a minimization problem, to a class of variational-hemivariational inequalities with perturbations in Banach spaces, which includes as a special case the class of mixed variational inequalities. Under very mild conditions, we establish some metric characterizations for the well-posed variational-hemivariational inequality, and show that the well-posedness by perturbations of a variational-hemivariational inequality is closely related to the well-posedness by perturbations of the corresponding inclusion problem. Furthermore, in the setting of finite-dimensional spaces we also derive some conditions under which the variational-hemivariational inequality is strongly generalized well-posed-like by perturbations.

In this paper we get estimation of the absolute condition number a Hilbert space operator, which is related with the outer generalized inverse of a given operator.

The aim of this paper is to study the existence and uniqueness of solutions for a general stochastic integrodifferential equation of the Ito type, by using the concept of non-linear bounded random integral contractors, which includes the Lipschitz condition as a special case. The method applied in this consideration follows partially the basic ideas of the contractor theory introduced earlier by Altman [1, 2] and Kuo [6]. It is also shown that the Lipschitz condition and the condition based on a bounded random integral contractor for the coefficients of the considered equation, in general, cannot be compared.

The comparison of differential operators is a problem that was formulated in sixties by Lars Hormander, it is a part of the theory of partial differential operators with constant coefficients, this problem up to now does not have a complete solution. The urgency of this problem is stipulated by the applications of the solvability theory of differential equations in special spaces of generalized functions. In this paper we prove some results in the manifold linearity of a polynomial, these results play an important role in the comparison of two linear partial differential operators problem.