Positive solutions for discrete boundary value problems involving the p-Laplacian with potential terms

In this paper, we discuss the existence and the uniqueness of discrete boundary value problems involving the p-Laplacian with potential terms. To this end, we deal with the strong comparison principle and the Dirichlet principle for the p-Laplacian with potential terms on weighted graphs with boundary. Moreover, we provide a lower bound of the potential terms which guarantees the existence of solutions of the boundary value problem for the operator. Finally, we also discuss inverse conductivity and potential problems for the operator.     

Existence and uniqueness theorems for fourth-order singular boundary value problems

By constructing a special cone and using cone compression and expansion fixed point theorem, the existence and uniqueness are established for the following singular fourth-order boundary value problems:

where f(t,x,y) may be singular at t=0,1; x=0 and y=0.     

Two generalizations of some fixed point theorems

The aim of this paper is to generalize two classical fixed point theorems given by Bogin [J. Bogin, A generalization of a fixed point theorem of Goebel, Kirk and Shimi, Canad. Math. Bull. 19 (1976) 7-12] and Greguš [M. Greguš, A fixed point theorem in Banach spaces, Boll. Un. Math. Ital. A (5) 17 (1980) 193-198]. We also complement and extend some very recent results proved by Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008) 1861-1869].     

Parametric fixed point algorithms with applications to economic policy analysis

Parametric fixed point algorithms are developed which construct the general equilibrium paths of continuous one-parameter families of economies. The algorithms are used to devise a dynamic framework for economic policy analysis in a general equilibrium setting. Applications to taxation policy issues are developed in detail.     

Ramsey-type theorems for metric spaces with applications to online problems

A nearly logarithmic lower bound on the randomized competitive ratio for the metrical task systems problem is presented. This implies a similar lower bound for the extensively studied K-server problem. The proof is based on Ramsey-type theorems for metric spaces, that state that every metric space contains a large subspace which is approximately a hierarchically well-separated tree (and in particular an ultrametric). These Ramsey-type theorems may be of independent interest.     

Using fixed point theorems to model the binding in protein-protein interactions

The binding in protein-protein interactions exhibits a kind of biochemical stability in cells. The mathematical notion of fixed points also describes stability. A point is a fixed point if it remains unchanged after a transformation by a function. Many points may not be a fixed point, but they may approach a stable status after multiple steps of transformation. In this paper, we define a point as a protein motif pair consisting of two traditional protein motifs. We propose a function and propose a method to discover stable motif pairs of this function from a large protein interaction, sequence data set. There are many interesting properties for this function (for example, the convergence). Some of them are useful for gaining much efficiency in the discovery of those stable motif pairs; some are useful for explaining why our proposed fixed point theorems are a good way to model the binding of protein interactions. Our results are also compared to biological results to elaborate the effectiveness, of our method.     

Two point hermite approximations for the solution of linear initial value and boundary value problems

Application of an idea originally due to Ch. Hermite allows the derivation of an approximate formula for expressing the integral ∫xixi?1y(x)dx as a linear combination of y(xi?1), y(xi), and their derivatives y(v)(xi?1) up to order v = α and y(v)(xi) up to order v = β. In addition to this integro-differential form a purely differential form of the 2-point Hermite approximation will be derived. Both types will be denoted by Hαβ-approximation. It will be shown that the well-known Obreschkoff-formulas contain no new elements compared to the much older Hαβ-method.The Hαβ-approximation will be applied to the solution of systems of ordinary differential equations of the type y'(x) = M(x)y(x) + q(x), and both initial value and boundary value problems will be treated. Function values at intermediate points x? (xi?1, xi) are obtained by the use of an interpolation formula given in this paper.An advantage of the Hαβ-method is the fact that high orders of approximation (α, β) allow an increase in step size hi. This will be demonstrated by the results of several test calculations.     

Some fixed point theorems in fuzzy normed linear spaces

In this paper, the concepts of sectional fuzzy continuous mappings, l-fuzzy compact sets, asymptotic fuzzy normal structure and strong uniformly convex fuzzy normed linear spaces have been introduced. Schauder-type and other fixed point theorems have been established in fuzzy normed linear spaces.     

Some fixed point theorems for maps with fuzzy distance in uniform space

The purpose of this paper is to define the notion of fuzzy A-distance in uniform spaces and give several new common fixed point results for weakly compatible contractive or expansive selfmappings on uniform spaces.     

Vlsi interconnection network for numerical solution of two point boundary value problems

We present the shooting parallel method implemented in systolic systems to solve Ordinary Differential Equations, taking advantage of the fact that this method may be greatly parallelised and that it generates diagonal or triangular sparse matrices.

The original problem is partitioned into subproblems whose individual size fit available systolic network dimensions. The network sizes depend on the order of the matrices used. The fitted technique is applied to halve the size of systolic networks used and therefore the sizes of networks are halved. We propose an organization scheme for the network interconnections.     

Sinc-Galerkin method for solving nonlinear weakly singular two point boundary value problems

A study of Sinc-Galerkin method based on double exponential transformation for solving a class of nonlinear weakly singular two point boundary value problems with non-homogeneous boundary conditions is given. The properties of the Sinc-Galerkin approach are utilized to reduce the computation of nonlinear problem to nonlinear system of equations with unknown coefficients. This method tested on several test examples. We compare our numerical results with several numerical results of existing methods. The demonstrated results confirm that proposed method is considerably efficient, accurate nature and rapidly converge.     

Strong convergence theorems based on a new modified extragradient method for variational inequality problems and fixed point problems in Banach spaces

In this paper, we introduce a new iterative algorithm by a modified extragradient method for finding a common element of the set of solutions of a general variational inequality and the set of common fixed points of an infinite family of k_i-strict pseudocontractions in a Banach space. We obtain some strong convergence theorems under suitable conditions. The results obtained in this paper improve and extend the recent ones announced by many others.     

Initial value methods for the primary two point boundary value problems in modeling viscoelastic flows

Initial value solvers through shooting methods will be used to compute solutions to the primary two-point boundary value problem arising in modeling viscoelastic flow. We will show that the classical Runge-Kutta methods will have at least h ²-order of convergence due to the presence of the singularity. Comparison with the work of others will also be presented through some numerical results and examples.     

Coupled fixed point theorems for mixed monotone mappings and an application to integral equations

In this paper, we extend the coupled fixed point theorems for a mixed monotone mapping F:X×X→X in partially ordered metric spaces established by Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006) 1379-1393]. An application to nonlinear integral equations is also given to illustrate our results.     

Some simple boundary value problems with corner singularities and boundary layers

Some boundary value problems for a second-order elliptic partial differential equation in a polygonal domain are considered. The highest order terms in the equation are multiplied by a small parameter, leading to a singularly perturbed problem. The singular perturbation causes boundary layers and interior layers in the solution, and the corners of the polygon cause corner singularities in the solution. The paper considers pointwise bounds for derivatives of the solution that show the influence of these layers and corner singularities. Several recent results on this problem are surveyed, and some open problems are stated and discussed.     

Integral boundary value problems with causal operators

This paper considers the existence of solutions for a class of integral boundary value problems with causal operators. We build a new comparison theorem. By utilizing the monotone iterative technique and the method of lower and upper solutions, we formulate sufficient conditions under which such problems have extremal or quasisolutions in a corresponding sector.     

Some common fixed point theorems for generalized nonlinear contractive mappings

Sufficient conditions for the existence of a common fixed point for generalized nonlinear contractive mappings are derived. As applications, some results on the set of best approximation for this class of mappings are also obtained. The proved results generalize and extend various known results in the literature.