Abstract and Applied Analysis


List of Papers (Total 406)

On boundary value problems for degenerate differential inclusions in Banach spaces

We consider the applications of the theory of condensing set-valued maps, the theory of set-valued linear operators, and the topological degree theory of the existence of mild solutions for a class of degenerate differential inclusions in a reflexive Banach space. Further, these techniques are used to obtain the solvability of general boundary value problems for a given class of...

Positive solutions of some nonlocal boundary value problems

We establish the existence of positive solutions of some m-point boundary value problems under weaker assumptions than previously employed. In particular, we do not require all the parameters occurring in the boundary conditions to be positive. Our results allow more general behaviour for the nonlinear term than being either sub- or superlinear.

Positive solutions for singular discrete boundary value problems

We study the existence of zero-convergent solutions for the second-order nonlinear difference equation Δ(anΦp(Δxn))=g(n,xn

A proximal point method for nonsmooth convex optimization problems in Banach spaces

In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric...

Uniform asymptotic normal structure, the uniform semi-Opial property and fixed points of asymptotically regular uniformly lipschitzian semigroups. Part I

In this paper we introduce the uniform asymptotic normal structure and the uniform semi-Opial properties of Banach spaces. This part is devoted to a study of the spaces with these properties. We also compare them with those spaces which have uniform normal structure and with spaces with WCS(X)>1.

On the existence of classical solutions for differential-functional IBVP

We consider the initial-boundary value problem for second order differential-functional equations of parabolic type. Functional dependence in the equation is of the Hale type. By using Leray-Schauder theorem we prove the existence of classical solutions. Our formulation and results cover a large class of parabolic problems both with a deviated argument and integro-differential...

Nonlinear ergodic theorems for a semitopological semigroup of non-Lipschitzian mappings without convexity

Let G be a semitopological semigroup, C a nonempty subset of a real Hilbert space H, and ℑ={Tt:t∈G} a representation of G as asymptotically nonexpansive type mappings of C into itself. Let L(x)={z∈H:infs∈Gsupt∈G‖Tts x−z‖=inft∈G‖Tt x−z‖} for each x∈C and L(ℑ)=∩x∈C L(x). In this paper, we prove that ∩s∈Gconv¯{Tts x:t∈G}∩L(ℑ) is nonempty for each x∈C if and only if there exists a...

Semilinear Volterra integrodifferential equations with nonlocal initial conditions

We establish the global existence of mild solutions to a class of nonlocal Cauchy problems associated with semilinear Volterra integrodifferential equations in a Banach space.

Homoclinic solutions for linear and linearizable ordinary differential equations

Using functional arguments, some existence results for the infinite boundary value problem x˙=F(t,x),x(−∞)=x(

On the projection constants of some topological spaces and some applications

We find a lower estimation for the projection constant of the projective tensor product X⊗ ∧Y and the injective tensor product X⊗ ∨Y, we apply this estimation on some previous results, and we also introduce a new concept of the projection constants of operators rather than that defined for Banach spaces.

The integral wavelet transform in weighted Sobolev spaces

The integral wavelet transform is defined in weighted Sobolev spaces, in which some properties of the transform as well as its asymptotical behaviour for small dilation parameter are studied.

Ordinary differential systems describing hysteresis effects and numerical simulations

We consider a general class of ordinary differential systems which describes input-output relations of hysteresis types, for instance, play or stop operators. The system consists of two first-order nonlinear ODEs and one of them includes a subdifferential operator depending on the unknowns. Our main objective of this paper is to give an existence-uniqueness result for the system...

On the modulus of u-convexity of Ji Gao

We consider the modulus of u-convexity of a Banach space introduced by Ji Gao (1996) and we improve a sufficient condition for the fixed-point property (FPP) given by this author. We also give a sufficient condition for normal structure in terms of the modulus of u-convexity.

Time-dependent Stokes equations with measure data

We establish the existence of a unique solution of an initial boundary value problem for the nonstationary Stokes equations in a bounded fixed cylindrical domain with measure data. Feedback laws yield the source and its intensity from the partial measurements of the solution in a subdomain.

New singular solutions of Protter's problem for the 3D wave equation

In 1952, for the wave equation,Protter formulated some boundary value problems (BVPs), which are multidimensional analogues of Darboux problems on the plane. He studied these problems in a 3D domain Ω0, bounded by two characteristic cones Σ1 and Σ2,0 and a plane region Σ0. What is the situation around these BVPs now after 50 years? It is well known that, for the infinite number...

On the modulus of U-convexity

We prove that the moduli of U-convexity, introduced by Gao (1995), of the ultrapower X˜ of a Banach space X and of X itself coincide whenever X is super-reflexive. As a consequence, some known results have been proved and improved. More precisely, we prove that uX(1)>0 implies that both X and the dual space X∗ of X have uniform normal structure and hence the “worth” property in...

Porosity and models with discrete innovations

In our previous work, we obtained sufficient conditions for the existence of trajectories with unbounded consumption for a model of economic dynamics with discrete innovations. In this paper, using the porosity notion, we show that for most models these conditions hold.

Properties of typical bounded closed convex sets in Hilbert space

For a nonempty separable convex subset X of a Hilbert space ℍ(Ω), it is typical (in the sense of Baire category) that a bounded closed convex set C⊂ℍ(Ω) defines an m-valued metric antiprojection (farthest point mapping) at the points of a dense subset of X, whenever m is a positive integer such that m≤dimX

Estimates on the Bergman Kernels in a Tangential Direction on Pseudoconvex Domains in

Let be a smoothly bounded pseudoconvex domain in and assume that where , the boundary of . Then we get optimal estimates of the Bergman kernel function along some “almost tangential curve“ .

Existence Theorems on Solvability of Constrained Inclusion Problems and Applications

Let be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space . Let be a maximal monotone operator and be bounded and continuous with . The paper provides new existence theorems concerning solvability of inclusion problems involving operators of the type provided that is compact or is of compact resolvents under weak boundary condition...

On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals

We introduce a new iterative method called D-iteration to approximate a fixed point of continuous nondecreasing functions on arbitrary closed intervals. The purpose is to improve the rate of convergence compared to previous work. Specifically, our main result shows that D-iteration converges faster than P-iteration and SP-iteration to the fixed point. Consequently, we have that D...

Generalized Fractional Integral Operators Involving Mittag-Leffler Function

The aim of this paper is to study various properties of Mittag-Leffler (M-L) function. Here we establish two theorems which give the image of this M-L function under the generalized fractional integral operators involving Fox’s -function as kernel. Corresponding assertions in terms of Euler, Mellin, Laplace, Whittaker, and -transforms are also presented. On account of general...

Numerical Simulation of a One-Dimensional Water-Quality Model in a Stream Using a Saulyev Technique with Quadratic Interpolated Initial-Boundary Conditions

The one-dimensional advection-diffusion-reaction equation is a mathematical model describing transport and diffusion problems such as pollutants and suspended matter in a stream or canal. If the pollutant concentration at the discharge point is not uniform, then numerical methods and data analysis techniques were introduced. In this research, a numerical simulation of the one...