Interpolation by integro quintic splines

Recently, Behforooz [1], has introduced a new approach to construct cubic splines by using the integral values, rather than the usual function values at the knots. Also he has established different sets of end conditions for cubic and quintic splines by using the integral values, see Behforooz [2], [3] and [4]. In this paper, we will use the same techniques of [1] to construct integro quintic splines. Although by using the integral values we expected to face a more complicated process for our construction, it turned out that the matrix of the system of linear equations that produces the parameters became a diagonally dominant matrix and the process became very simple. The selection of the required end conditions for our integro quintic splines will be discussed. The numerical examples and computational results illustrate and guarantee a higher accuracy for this approximation.     

Majorizing functions and two-point Newton-type methods

The semi-local convergence of a Newton-type method used to solve nonlinear equations in a Banach space is studied. We also give, as two important applications, convergence analyses of two classes of two-point Newton-type methods including a method mentioned in [5] and the midpoint method studied in [1], [2] and [12]. Recently, interest has been shown in such methods [3] and [4].     

The matching theorems in G-convex spaces with applications

The purpose of this paper is to establish some new matching theorems in G-convex spaces and, as applications, to obtain some new fixed point theorems, section theorems and a minimax theorem in G-convex spaces. The results presented in this paper improve and generalize the corresponding results in [1], [2], [3], [4], [5], [7], [8], [9], [10], [11] and [12].     

Fixed points and exponential stability for stochastic Volterra-Levin equations

In this paper we study a stochastic Volterra-Levin equation. By using fixed point theory, we give some conditions for ensuring that this equation is exponentially stable in mean square and is also almost surely exponentially stable. Our result generalizes and improves on the results in [14], [1] and [30].     

Kantorovich-type semilocal convergence analysis for inexact Newton methods

We provide a new semilocal convergence analysis for generating an inexact Newton method converging to a solution of a nonlinear equation in a Banach space setting. Our analysis is based on our idea of recurrent functions. Our results are compared favorably to earlier ones by others and us (Argyros (2007, 2009) [5] and [6], Argyros and Hilout (2009) [7], Guo (2007) [15], Shen and Li (2008) [18], Li and Shen (2008) [19], Shen and Li (2009) [20]). Numerical examples are provided to show that our results apply, but not earlier ones [15], [18], [19] and [20].     

A unifying theorem for Newton’s method on spaces with a convergence structure

We present a semilocal convergence theorem for Newton’s method (NM) on spaces with a convergence structure. Using our new idea of recurrent functions, we provide a tighter analysis, with weaker hypotheses than before and with the same computational cost as for Argyros (1996, 1997, 1997, 2007) [1], [2], [3] and [5], Meyer (1984, 1987, 1992) [13], [14] and [15]. Numerical examples are provided for solving equations in cases not covered before.     

Exponential stability of periodic neural networks with impulsive effects and time-varying delays

By employing Young inequality and constructing suitable Liapunov functions, we investigate the existence and globally exponential stability of periodic neural networks with impulses and time-varying delays. The results extend and improve some earlier ones [1], [5] and [12]. An illustrative example and simulations are given to show the validity of the main results.     

Weak convergence conditions for Inexact Newton-type methods

We establish a new semilocal convergence results for Inexact Newton-type methods for approximating a locally unique solution of a nonlinear equation in a Banach spaces setting. We show that our sufficient convergence conditions are weaker and the estimates of error bounds are tighter in some cases than in earlier works [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30] and [31]. Special cases and numerical examples are also provided in this study.     

Approximation of signals of class Lip(α, p) by linear operators

Mittal, Rhoades [5], [6], [7] and [8] and Mittal et al. [9] and [10] have initiated a study of error estimates E_n(f) through trigonometric-Fourier approximation (tfa) for the situations in which the summability matrix T does not have monotone rows. In this paper we continue the work. Here we extend two theorems of Leindler [4], where he has weakened the conditions on {p_n} given by Chandra [2], to more general classes of triangular matrix methods. Our Theorem also partially generalizes Theorem 4 of Mittal et al. [11] by dropping the monotonicity on the elements of matrix rows, which in turn generalize the results of Quade [15].     

Quasi-separatrix layers and three-dimensional reconnection diagnostics for line-tied tearing modes

In three-dimensional magnetic configurations for a plasma in which no closed field line or magnetic null exists, no magnetic reconnection can occur, by the strictest definition of reconnection. A finitely long pinch with line-tied boundary conditions, in which all the magnetic field lines start at one end of the system and proceed to the opposite end, is an example of such a system. Nevertheless, for a long system of this type, the physical behavior in resistive magnetohydrodynamics (MHD) essentially involves reconnection. This has been explained in terms comparing the geometric and tearing widths [1] and [2]. The concept of a quasi-separatrix layer [3] and [4] was developed for such systems. In this paper we study a model for a line-tied system in which the corresponding periodic system has an unstable tearing mode. We analyze this system in terms of two magnetic field line diagnostics, the squashing factor [5], [6] and [7] and the electrostatic potential difference [8] and [9] which has been used in kinematic reconnection studies. We discuss the physical and geometric significance of these two diagnostics and compare them in the context of discerning tearing-like (reconnection-like) behavior in line-tied modes.     

Monotonic positive solution of a nonlinear quadratic functional integral equation

The existence of positive monotonic solutions, in the class of continuous functions, for some nonlinear quadratic integral equation have been studied in [4], [5], [6], [7] and [8]. Here we are concerning with a nonlinear quadratic integral equation of Volterra type and we shall prove the existence of at least one L₁-positive monotonic solution for that equation under Carathèodory condition.     

Convergence of Directional Methods under mild differentiability and applications

A semilocal convergence analysis for Directional Methods under mild differentiability conditions is provided in this study. Using our idea of recurrent functions, we provide sufficient convergence conditions as well as the corresponding errors bounds. The results are extended to hold in a Hilbert space setting and a favorable comparison is provided with earlier works [6], [7], [8], [9], [10], [11] and [20]. Numerical examples are also provided in this study.     

Double Hall algebras and derived equivalences

We show that the reduced Drinfeld double of the Ringel-Hall algebra of a hereditary category is invariant under derived equivalences. By associating an explicit isomorphism to a given derived equivalence, we also extend the results of Burban and Schiffmann [5] and [006], Sevenhant and Van den Bergh (1999) [25], and Xiao and Yang (2001) [31].     

On recent developments in the theory of abstract differential equations with fractional derivatives

This note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives. We show that the existence results in [Agarwal et al. (2009) [1], Belmekki and Benchohra (2010) [2], Darwish et al. (2009) [3], Hu et al. (2009) [4], Mophou and N’Guérékata (2009) [6] and [7], Mophou (2010) [8] and [9], Muslim (2009) [10], Pandey et al. (2009) [11], Rashid and El-Qaderi (2009) [12] and Tai and Wang (2009) [13]] are incorrect since the considered variation of constant formulas is not appropriate. In this note, we also consider a different approach to treat a general class of abstract fractional differential equations.     

Some convergence theorems of non-implicit iteration process with errors for a finite families of I-asymptotically nonexpansive mappings

The purpose of this paper is to study the weak and strong convergence of non-implicit iteration process with errors to a common fixed point for a finite family of I-asymptotically quasi-nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of several authors [1], [2], [7], [8], [9], [10], [11], [12], [13], [14], [17], [19], [22], [23], [24], [25], [26], [27], [28] and [29].     

Fixed point theorems for some generalized multivalued nonexpansive mappings

In this paper, we introduce a condition on multivalued mappings which is a multivalued version of condition (C_λ) defined by Garcia-Falset et al. (2011) [3]. It is shown here that some of the classical fixed point theorems for multivalued nonexpansive mappings can be extended to mappings satisfying this condition. Our results generalize the results in Lim (1974), Lami Dozo (1973), Kirk and Massa (1990), Garcia-Falset et al. (2011), Dhompongsa et al. (2009) and Abkar and Eslamian (2010) [4], [5], [6], [3], [7] and [8] and many others.     

Stability in cellular neural networks with a piecewise constant argument

In this paper, by using the concept of differential equations with piecewise constant arguments of generalized type [1], [2], [3] and [4], a model of cellular neural networks (CNNs) [5] and [6] is developed. The Lyapunov-Razumikhin technique is applied to find sufficient conditions for the uniform asymptotic stability of equilibria. Global exponential stability is investigated by means of Lyapunov functions. An example with numerical simulations is worked out to illustrate the results.     

Coderivatives of normal cone mappings and Lipschitzian stability of parametric variational inequalities

In this paper, we provide a comprehensive study of coderivative formulas for normal cone mappings. This allows us to derive necessary and sufficient conditions for the Lipschitzian stability of parametric variational inequalities in reflexive Banach spaces. Our development not only gives an answer to the open questions raised in Yao and Yen (2009) [11], but also establishes generalizations and complements of the results given in Henrion et al. (2010) [4] and Yao and Yen (2009) [11] and [12].     

Unbounded critical points for a class of lower semicontinuous functionals

For a general class of lower semicontinuous functionals, we prove existence and multiplicity of critical points, which turn out to be unbounded solutions to the associated Euler equation. We apply a nonsmooth critical point theory developed in [10], [12] and [13] and applied in [8], [9] and [20] to treat the case of continuous functionals.