Common Fixed Point Results for Quasi-contractions Involving Altering Distance Functions in Ordered Cone Metric Spaces

Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition for the uniqueness of common fixed point is proved. Also, an example is given to support our results.

Adaptive broadband beamformer for nonuniform linear array based on second order cone programming

Adaptive broadband beamforraing is a key issue in array applications. The adaptive broadband beamformer with tapped delay line （TDL） structure for nonuniform linear array （NLA） is designed according to the rule of minimizing the beamformer＇s output power while keeping the distortionless response （DR） in the direction of desired signal and keeping the constant beamwidth （CB） with the prescribed sidelobe level over the whole operating band. This kind of beamforming problem can be solved with the interior-point method after being converted to the form of standard second order cone programming （SOCP）. The computer simulations are presented which illustrate the effectiveness of our beamformer.

Iterative Solution for Systems of Binary Non-mixed Monotone Operator Equations

With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.

SRV constraint based FIB design for wideband linear array

Frequency-invariant beamformer （FIB） design is a key issue in wideband array signal processing. To use commonly wideband linear array with tapped delay line （TDL） structure and complex weights, the FIB design is provided according to the rule of minimizing the sidelobe level of the beampattern at the reference frequency while keeping the distortionless response constraint in the mainlobe direction at the reference frequency, the norm constraint of the weight vector and the amplitude constraint of the averaged spatial response variation （SRV）. This kind of beamformer design problem can be solved with the interior-point method after being converted to the form of standard second order cone programming （SOCP）. The computer simulations are presented which illustrate the effectiveness of our FIB design method for the wideband linear array with TDL structure and complex weights.

Iterative Solutions for a Non-monotone BinaryOperator Equations and Operator System of Equations

By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A1+A2, B=B1+B2,A1 and B1 are mixed monotone, A2 and B2 are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.

ITERATIVE SOLUTIONS FOR SYSTEMS OF NONLINEAR OPERATOR EQUATIONS IN BANACH SPACE

By using partial order method, the existence, uniqueness and iterative approximation of solutions for a class of systems of nonlinear operator equations in Banach space are discussed. The results obtained in this paper extend and improve recent results.

COUPLED FIXED POINTS OF SKEW INCREASINGOPERATORS AND APPLICATIONS

In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative formula are given.

Existence and Uniqueness of Solution of Some Increasing Operators and Applications

By using the cone theory and the monotone succession skills, it is studied the existence uniqueness of fixed point for a class of increasing operators without continuity and compactness and concave or convex conditions in Banach spaces. The results presented here improve and generalize some corresponding results for increasing operator.

GLOBAL SOLUTIONS OF SYSTEMS OF NONLINEAR IMPULSIVE VOLTERRA INTEGRAL EQUATIONS IN BANACH SPACES

The existence of solutions for systems of nonlinear impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces is studied. Some existence theorems of extremal solutions are obtained, which extend the related results for this class of equations on a finite interval with a finite. number of moments of impulse effect. The results are demonstrated by means of an example of an infinite systems for impulsive integral equations.

EXISTENCE OF SOLUTIONS FOR MIXED MONOTONE IMPULSIVE VOLTERRA INTEGRAL EQUATIONS IN BANACH SPACES

This paper studies the existence of solutions for mixed monotone impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces. By using the mixed monotone iterative technique and Monch fixed point theorem, Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained. Finally, an example is worked out.

EXISTENCE THEOREMS OF SOLUTIONS FOR NONLINEAR IMPULSIVE VOLTERRA INTEGRAL EQUATIONS IN BANACH SPACES

In this paper,the Monch fixed point theorem and an impulsive integral inequality is used to prove some existence theorems of solutions for nonlinear impulsive Volterra integral equations in Banach spaces that improve and extend the previous results.

Second order duality for multiobjective programming with cone constraints

We focus on second order duality for a class of multiobjective programming problem subject to cone constraints. Four types of second order duality models are formulated. Weak and strong duality theorems are established in terms of the generalized convexity, respectively. Converse duality theorems, essential parts of duality theory, are presented under appropriate assumptions. Moreover, some deficiencies in the work of Ahmad and Agarwal(2010) are discussed.

Existence of Positive Solutions for Systems of Nonlinear Second-Order Differential Equations on the Half Line in a Banach Space

In this paper, the cone theory and MSnch fixed point theorem combined with the monotone iterative technique are used to investigate the positive solutions for a class of systems of nonlinear singular differential equations with multi-point boundary value conditions on the half line in a Banach space. The conditions for the existence of positive solutions are formulated. In addition, an explicit iterative approximation of the solution is also derived.

EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM

The existence and multiplicity of positive solutions to a periodic boundary value problem for nonlinear third-order ordinary differential equation are established, based on the zero point theorem concerning cone expansion and compression of order type. Our main approach is different from the previous papers on the existence of multiple positive solutions to the similar problem.

Side-lobe constrained beamforming under virtual expansion of L-shaped array

To reduce the side-lobe level of L-shaped expansion array and improve the output signal to interference and noise ratio(SINR),the algorithm of side-lobe constraint based on minimum variance distortionless response(MVDR-SC)is proposed.Firstly,the approach of mixing diagonal loading and Mailloux-Zatman(DLMZ)is used to taper the covariance matrix of the expansion array.Then,the second order cone programming(SOCP)obtained by constructing a new matrix is used to control the beam side-lobe.Finally,the new adaptive weight numbers are constructed by adjusting the proportion between DLMZ and SOCP.Simulation results show that the MVDR-SC algorithm can effectively reduce the side-lobe of beamforming under the L-shaped expansion array and obtain a larger output SINR.At the same time,it has good robustness to the mutual coupling error.