Applied Analysis Research Papers - Academia.edu (original) (raw)

2007, Journal of Applied Analysis

The solvability of the generalized weak vector implicit variational inequality problem, generalized strong vector implicit variational inequality problem and generalized vector variational inequality problem are proved by using a... more

2001, Journal of Mathematical Analysis and Applications

New classes of generalized (F, ρ)-convexity are introduced for vector-valued functions. Examples are given to show their relations with (F, ρ)-pseudoconvex, (F, ρ)-quasiconvex, and strictly (F, ρ)-pseudoconvex vector-valued functions. The sufficient optimality conditions and duality results are obtained for multiobjective programming involving generalized (F, ρ)-convex vector-valued functions.

2005, Journal of Applied Analysis

Fritz John and Kuhn-Tucker type necessary optimality conditions for a Pareto optimal (efficient) solution of a multiobjective control problem are obtained by first reducing the multiobjective control problem to a system of single objective control problems, and then using already established optimality conditions. As an application of Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir type dual multiobjective control problems are formulated and usual duality results are established under invexity/generalized invexity, relating properly efficient solutions of the primal and dual problems. Wolfe and Mond-Weir type dual multiobjective control problems with free boundary conditions are also presented.

2012, Nonlinear Analysis: Theory, Methods & Applications

Keywords: Multiobjective fractional programming Locally Lipschitz function Generalized subdifferential Exponential V -r-invexity Duality a b s t r a c t This paper is to study a subdifferentiable multiobjective fractional programming problem under exponential V -r-invexity. We establish sufficient optimality conditions for multiobjective fractional programming problems involving exponential V -r-invex Lipschitz functions. By optimality conditions, the parametric dual model is formulated. Consequently, the duality theorems are proved so that the optimal values of the duality problems are equal to the primary problem under the framework of exponential V -rinvexity for the Lipschitz function.

Tamkang Journal of Mathematics

1997, Journal of Applied Analysis

We use the method of norms on possibilities to answer a question of Kunen and construct a ccc σ-ideal on 2 ω with various closure properties and distinct from the ideal of null sets, the ideal of meager sets and their intersection.

2000, Journal of Applied Analysis

Using the Wright's generalized hypergeometric function, we investigate a class W (q, s; A, B, λ) of analytic functions with negative coefficients. We derive many results for the modified Hadamard product of functions belonging to the class W (q, s; A, B, λ). Moreover, we generalize some of the distortion theorems to the classical fractional integrals and derivatives and the Saigo (hypergeometric) operators of fractional calculus.

2000, Journal of Applied Analysis

In this paper we shall consider the nonlinear neutral delay differential equations with variable coefficients. Some new sufficient conditions for oscillation of all solutions are obtained. Our results extend and improve some of the well known results in the literature. Some examples are considered to illustrate our main results. The neutral logistic equation with variable coefficients is considered to give some new sufficient conditions for oscillation of all positive solutions about its positive steady state.

1999, Mathematical Methods in the Applied Sciences

We consider a mathematical model which describes the frictional contact between a deformable body and an obstacle, say a foundation. The body is assumed to be linear elastic and the contact is modeled with a version of Coulomb's law of dry friction in which the normal stress is prescribed on the contact surface. The novelty consists here in the fact that we consider a slip dependent coefficient of friction and a quasistatic process. We present two alternative yet equivalent formulations of the problem and establish existence and uniqueness results. The proofs are based on a new result obtained in in the study of evolutionary variational inequalities.

2000, Journal of Applied Analysis

A functional equation related to a problem of linear dependence of iterates is considered.

Journal of Applied Analysis

In this paper, we develop two-step collocation (2-SC) methods to solve two-dimensional nonlinear Volterra integral equations (2D-NVIEs) of the second kind. Here we convert a 2D-NVIE of the second kind to a one-dimensional case, and then we solve the resulting equation numerically by two-step collocation methods. We also study the convergence and stability analysis of the method. At the end, the accuracy and efficiency of the method is verified by solving two test equations which are stiff. In examples, we use the well-known differential transform method to obtain starting values.

2001, … IN APPLIED ANALYSIS

This paper is concerned with the asymptotic behavior in time of solutions to a linear problem arising in the theory of heat conduction with memory. In a rigid heat conductor obeying the Gurtin-Pipkin constitutive model for the heat flux, the energy balance leads to an hyperbolic, linear integro-differential equation. In spite of the presence of a convolution term, the homogeneous original problem, subject to initial-history conditions, is transformed into an autonomous system by a suitable choice of variables. By means of semigroup techniques the exponential decay of solutions is provided. When a time-dependent heat supply is present, this result allows us to obtain the existence of a uniform absorbing set for the process associated to the problem.

2000, Journal of Applied Analysis

In [9], the present authors and Richard O'Malley showed that in order for a function be universally polygonally approximable it is necessary that for each ε > 0, the set of points of non-quasicontinuity be σ − (1 − ε) symmetrically porous. The question as to whether that condition is sufficient or not was left open. Here we prove that if a set, E = ∞ n=1 En, such that each Ei is closed and 1-symmetrically porous, then there is a universally polygonally approximable function, f , whose set of points of non-quasicontinuity is precisely E. Although it is tempting to call this a partial converse to our earlier theorem it might be more since it is not known if these two notions of symmetric porosity differ in the class of Fσ sets.

2008, Journal of Applied Analysis

A nonlinear multiobjective programming problem is considered. Weak, strong and strict converse duality theorems are established under generalized second order (F, α, ρ, d)-convexity for second order Mangasarian type and general Mond-Weir... more

2000, Journal of Applied Analysis

We consider the problem utt + δut + εa∆u + ϕ(Ω |∇u| 2 dx)∆u ≥ f (x, t), posed in Ω × (0, +∞). Here Ω ⊂ R N is a an open smooth bounded domain and ϕ is like ϕ(s) = bs γ , γ > 0, a > 0 and ε = ±1. We prove, in certain conditions on f and ϕ that there is absence of global solutions. The method of proof relies on a simple analysis of the ordinary inequality of the type w + δw ≥ αw + βw p. It is also shown that a global positive solution, when it exists, must decay at least exponentially.

2005, Journal of Applied Analysis

We prove the existence of weak solutions for some quasilinear elliptic reaction-diffusion systems with Dirichlet boundary conditions and satisfying to the two main properties: the positivity of the solutions and the balance law. The... more

2003, Journal of …

We study MB-representations of algebras and ideals when they are relativized to a subset, and when one considers the operations of sum and intersection for families of algebras and ideals. We observe that the algebras ∆ 0 α , 3 ≤ α < ω1, on R are MB-representable under GCH. We find a class of topological spaces in which the algebra of clopen sets is MB-representable.

2000, Journal of Applied Analysis

We analyze term-by-term differentiability of uniformly convergent series of the form

2000, Journal of Applied Analysis

In the paper we present two continuous selection theorems in hyperconvex metric spaces and apply these to study fixed point and coincidence point problems as well as variational inequality problems in hyperconvex metric spaces.

2000, Journal of Applied Analysis

This article is concerned with the existence result of the unilateral problem associated to the equations of the type Au − divφ(u) = f ∈ L 1 (Ω), where A is a Leray-Lions operator having a growth not necessarily of polynomial type and φ ∈... more

2000, Journal of Applied Analysis

We are going to prove an extension theorem on a functional equation for special means studied by Domsta and Matkowski.

2000, Journal of Applied Analysis

In this paper, we study fixed points of solutions of the differential equation

2000, Journal of Applied Analysis

In this paper, an existence result of quasi-equilibrium problem is proved and used to establish the existence of weighted Nash equilibria for constrained multi-criteria games under a generalized quasiconvexity condition and a coercivity type condition on the payoff functions. As consequence, we prove the existence of Pareto equilibria for constrained multi-criteria games with non-compact strategy sets in topological vector spaces.

2006, Journal of Applied Analysis

Abstract. In the first part of this paper, we prove a minimax inequal-ity for maps satisfying a generalized coercivity type condition. As a consequence, we prove a result on the solvability of complementarity problems. In the second part,... more

2000, Journal of Applied Analysis

The existence of at least one solution to a nonlinear second order differential equation in R k on the semi-infinite with the first derivative vanishing at infinity is proved by using topological methods. The second boundary condition is... more

2000, Journal of Applied Analysis

We introduce the notion of a random partition of the stochastic interval [τ0, τ∞] as an analogy to the classical case and characterize the predictable processes associated with such partitions. Also we identify the operator algebras... more

2000, Journal of Applied Analysis

A σ-finite Borel measure in a topological space is called residual if each nowhere dense set has measure zero. We show that in various types of spaces without isolated points there are no residual measures. Among these spaces are e.g. σ-spaces, locally metrizable spaces, locally separable spaces, spaces that have a σ-point-finite πbase, submanifolds.

2001

We consider the numerical solution of quasilinear elliptic Neumann problems. The basic diculty is the non-injectivity of the operator, which can be overcome by suitable factorization. We extend the gradient-nite element method (GFEM), introduced earlier by the authors for Dirichlet problems, to the Neumann problem. The algorithm is constructed and its convergence is proved.

2000, Journal of Applied Analysis

It is known that the following two fundamental properties of porosity fail for symmetric porosity: 1) Every nowhere dense set A contains a residual subset of points x at which A has porosity 1. 2) If A is a porous set and 0 < p < 1, then A can be written as a countable union of sets, each of which has porosity at least p at each of its points. Here we explore the somewhat surprising extent to which these properties fail to carry over to the symmetric setting and investigate what symmetric analogs do hold. 1991 Mathematics Subject Classification. 26A21.

2000, Journal of Applied Analysis

We prove that if a pair I, J of ccc, translation invariant σ-ideals on 2 ω has the Fubini Property, then I = J. This leads to a slightly improved exposition of a part of the Farah-Zapletal proof of an invariant version of their theorem which characterizes the measure and category σ-ideals on 2 ω as essentially the only ccc definable σ-ideals with Fubini Property.

Journal of Applied Analysis

We deal with the wave equation with assigned moving boundary (

2002, Journal of Applied Analysis

In this paper, nonlocal in time problem for abstract evolution equation of second order is studied and theorem on existence and uniqueness of its solution is proved. Some applications of this theorem for hyperbolic partial differential equations and systems are considered and it is proved, that well-posedness of the mentioned problems depends on algebraic properties of ratios between the dimensions of the spatial boundary and the times appearing in the nonlocal in time initial conditions.

2000, Journal of Applied Analysis

In this paper we consider the Hadamard product of regular functions using the concept of subordination. Let P (A, B) denote the class of regular functions subordinated to the linear fractional transfor-

2000, Journal of Applied Analysis

We show that for a σ-finite diffused Borel measure in a nondiscrete locally bounded topological group there is a meager set whose complement is of measure zero.

2000, Journal of Applied Analysis

Under reasonable assumptions on the data u, v and the function f , we show that the nonlinear periodic Goursat problem ∂ 2 u ∂x∂y (x, y) = f (x, y, u(x, y)); u(x, 0) = v(x); u(0, y) = w(y) which cannot be posed in the general theory of distributions, may be studied and solved in a differential algebra of periodic new generalized functions on R 2. This algebra contains, in a canonical way, the space of periodic distributions on R 2 as a linear subspace. When the data are Dirac measures, a particular study is done, showing the nature of the singularities involved in this case.

2000, Journal of Applied Analysis

Two equivalent metrics can be compared, with respect to their uniform properties, in several different ways. We present some of them, and then use one of these conditions to characterize which metrics on a space induce the same lower... more

1995, Journal of Applied Analysis

2000, Journal of Applied Analysis

We investigate the topological entropy of a green interval map. Defining the complexity we estimate from above the topological entropy of a green interval map with a given complexity. The main result of the paper-stated in Theorem... more

2005, Journal of Applied Analysis

This paper proposes an inductive method to construct bases for spaces of spherical harmonics over the unit sphere Ω2q of C q . The bases are shown to have many interesting properties, among them orthogonality with respect to the inner product of L 2 (Ω2q). As a bypass, we study the inner product [f, g] = f (D)(g(z))(0) over the space P(C q ) of polynomials in the variables z, z ∈ C q , in which f (D) is the differential operator with symbol f (z). On the spaces of spherical harmonics, it is shown that the inner product [·, ·] reduces to a multiple of the L 2 (Ω2q) inner product. Bi-orthogonality in (P(C q ), [·, ·]) is fully investigated.

2007, Journal of Applied Analysis

2007, … in Applied Analysis

ABSTRACT: We consider an integro-differential equation, proposed in the literature as a model of neuronal activity. We establish conditions under which an initial activity function exhibiting localized pattern formation completely... more

Communications in Applied Analysis

In this paper, a fixed point theorem for absolute retract is used to investigate the existence of fuzzy solutions for first and second order impulsive ordinary differential equations.