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In this paper, we introduce a new iterative method in a real Hilbert space for approximating a point in the solution set of a pseudomonotone equilibrium problem which is a common fixed point of a finite family of demicontractive mappings. Our result does not require that we impose the condition that the sum of the control sequences used in the finite convex combination is equal to 1. Furthermore, we state and prove a strong convergence result and give some numerical experiments to demonstrate the efficiency and applicability of our iterative method. [ABSTRACT FROM AUTHOR]

In this paper we put forward a family of algorithms for lifting solutions of a polynomial congruence mod p to polynomial congruence mod pk. For this purpose, root-fin ding iterative methods are employed for solving polynomial congruences of the form axn ≡ b(mod pk), k ≥ 1, where a, b, and n > 0 are integers which are not divisible by an odd prime p. It is shown that the algorithms suggested in this paper drastically reduce the complexity for such computations to a logarithmic scale. The efficacy of the proposed technique for solving negative exponent equations of the form axn ≡ b(mod pk) has also been addressed. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is first to introduce the concept of total asymptotically nonexpansive mappings and to prove a Δ-convergence theorem for finding a common fixed point of the total asymptotically nonexpansive mappings and the asymptotically nonexpansive mappings. The demiclosed principle for this kind of mappings in CAT(0) space is also proved in the paper. Our results extend and improve many results in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish a strong convergence of a new parallel iterative algorithm with mean errors to a common fixed point for two finite families of C'iric' quasi-contractive operators in normed spaces. The results presented in this paper generalize and improve the corresponding results of Berinde, Gu, Rafiq, Rhoades, and Zamfirescu. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present the notion of weak relatively nonexpansive multivalued mapping and to prove the strong convergence theorems of fixed point for weak relatively nonexpansive multivalued mappings in Banach spaces. The weak relatively nonexpansive multivalued mappings are more generalized than relatively nonexpansive multivalued mappings. In this paper, an example will be given which is a weak relatively nonexpansive multivalued mapping but not a relatively nonexpansive multivalued mapping. In order to get the strong convergence theorems for weak relatively nonexpansive multivalued mappings, a new monotone hybrid iteration algorithm with generalized (metric) projection is presented and is used to approximate the fixed point of weak relatively nonexpansive multivalued mappings. In this paper, the notion of multivalued resolvent of maximal monotone operator has been also presented which is a weak relatively nonexpansive multivalued mapping and can be used to find the zero point of maximal monotone operator. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new Kirk type iterative algorithm called Kirk multistep iteration and to study its convergence. We also prove some theorems related to the stability results for the Kirk multistep and Kirk-SP iterative processes by employing certain contractive-like operators. Our results generalize and unify some other results in the literature. [ABSTRACT FROM AUTHOR]

This paper is concerned with iterative solution to a class of the real coupled matrix equations. By using the hierarchical identification principle, a gradient-based iterative algorithm is constructed to solve the real coupled matrix equations A1XB1 + A2XB2 = F1 and C1XD1 + C2XD2 = F2. The range of the convergence factor is derived to guarantee that the iterative algorithm is convergent for any initial value. The analysis indicates that if the coupled matrix equations have a unique solution, then the iterative solution converges fast to the exact one for any initial value under proper conditions. A numerical example is provided to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Cost-sensitive support vector machine is one of the most popular tools to deal with class-imbalanced problem such as fault diagnosis. However, such data appear with a huge number of examples as well as features. Aiming at class-imbalanced problem on big data, a cost-sensitive support vector machine using randomized dual coordinate descent method (CSVM-RDCD) is proposed in this paper. The solution of concerned subproblem at each iteration is derived in closed form and the computational cost is decreased through the accelerating strategy and cheap computation. The four constrained conditions of CSVM-RDCD are derived. Experimental results illustrate that the proposed method increases recognition rates of positive class and reduces average misclassification costs on real big class-imbalanced data. [ABSTRACT FROM AUTHOR]

The matrix equation ..., which includes some frequently investigated matrix equations as its special cases, plays important roles in the system theory. In this paper, we propose an iterative algorithm for solving the quaternion matrix equation ... over generalized (P,Q)-reflexivematrices. The proposed iterative algorithmautomatically determines the solvability of the quaternion matrix equation over generalized (P,Q)-reflexive matrices. When the matrix equation is consistent over generalized (P,Q)-reflexive matrices, the sequence {X(k)} generated by the introduced algorithm converges to a generalized (P,Q)-reflexive solution of the quaternion matrix equation. And the sequence {X(k)} converges to the least Frobenius normgeneralized (P,Q)-reflexive solution of the quaternionmatrix equation when an appropriate initial iterativematrix is chosen. Furthermore, the optimal approximate generalized (P,Q)-reflexive solution for a given generalized (P,Q)-reflexive matrix X0 can be derived. The numerical results indicate that the iterative algorithm is quite efficient. [ABSTRACT FROM AUTHOR]

This paper deals with a new iterative algorithm {xn} with a strongly positive operator A for a k-strict pseudo-contraction T and a non-self-Lipschitzian mapping S in Hilbert spaces. Under certain appropriate conditions, the sequence {xn} converges strongly to a fixed point of T, which solves some variational inequality. The results here improve and extend some recent related results. [ABSTRACT FROM AUTHOR]

We propose synchronal algorithm and cyclic algorithm based on the general iterative method for solving a hierarchical fixed point problem. Under suitable parameters, the iterative sequence converges strongly to a common fixed point of N nonexpansive mappings and also the unique solution of a variational inequality. The results presented in this paper improve and extend the corresponding results reported recently by some authors. Furthermore, a numerical example is given to demonstrate the effectiveness of our iterative schemes. [ABSTRACT FROM AUTHOR]

Inspired by the note on split common fixed-point problem for quasi-nonexpansive operators presented by Moudafi (2011), based on the very recent work by Dang et al. (2012), in this paper, we propose an inertial iterative algorithm for solving the split common fixed-point problem for quasi-nonexpansive operators in the Hilbert space. We also prove the asymptotical convergence of the algorithm under some suitable conditions. The results improve and develop previously discussed feasibility problems and related algorithms. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce and analyze the Mann-type extragradient iterative algorithms with regularization for finding a common element of the solution set Ξ of a general system of variational inequalities, the solution set Γ of a split feasibility problem, and the fixed point set Fix(S) of a strictly pseudocontractive mapping S in the setting of the Hilbert spaces. These iterative algorithms are based on the regularization method, the Mann-type iteration method, and the extragradient method due to Nadezhkina and Takahashi (2006). Furthermore, we prove that the sequences generated by the proposed algorithms converge weakly to an element of Fix(S) ∩ Ξ ∩ Γ under mild conditions. [ABSTRACT FROM AUTHOR]

This paper is concerned with the higher order nonlinear neutral delay differential equation ..., for all t ≥ t0. Using the Banach fixed point theorem, we establish the existence results of uncountablymany positive solutions for the equation, construct Mann iterative sequences for approximating these positive solutions, and discuss error estimates between the approximate solutions and the positive solutions. Nine examples are included to dwell upon the importance and advantages of our results. [ABSTRACT FROM AUTHOR]

The generalized coupled Sylvester systems play a fundamental role in wide applications in several areas, such as stability theory, control theory, perturbation analysis, and some other fields of pure and applied mathematics. The iterative method is an important way to solve the generalized coupled Sylvester systems. In this paper, an iterative algorithm is constructed to solve the minimum Frobenius norm residual problem: ... min over generalized reflexive matrix X. For any initial generalized reflexive matrix X1, by the iterative algorithm, the generalized reflexive solution X* can be obtained within finite iterative steps in the absence of round-off errors, and the unique least-norm generalized reflexive solution X* can also be derived when an appropriate initial iterative matrix is chosen. Furthermore, the unique optimal approximate solution ... to a given matrix X0 in Frobenius norm can be derived by finding the least-norm generalized reflexive solution ...* of a new corresponding minimum Frobenius norm residual problem: min ... with ... Finally, several numerical examples are given to illustrate that our iterative algorithm is effective [ABSTRACT FROM AUTHOR]

The purpose of this article is to present a general viscosity iteration process {xn} which defined by xn + 1 = (I - anA)Txn + ßn?f(xn) + (an - ßn)xn and to study the convergence of {xn}, where T is a nonexpansive mapping and A is a strongly positive linear operator, if {an}, {ßn} satisfy appropriate conditions, then iteration sequence {xn} converges strongly to the unique solution x* ∈ f(T) of variational inequality ((A-?f)x*,x-x*) = 0,forallx ∈ f(T). Meanwhile, a approximate iteration algorithm is presented which is used to calculate the fixed point of nonexpansive mapping and solution of variational inequality, the error estimate is also given. The results presented in this paper extend, generalize, and improve the results of Xu, G. Marino and Xu and some others. [ABSTRACT FROM AUTHOR]

This paper deals with a new iterative algorithm for solving hierarchical fixed point problems of an infinite family of pseudocontractions in Hilbert spaces by yn = βnSxn + (1 - βn)xn, xn+1 = PC[αnf(xn) + (1 - αn)Σi=1∞ μi(n) Tiyn], and ∀n = 0, where Ti : C ↦ H is a nonself ki-strictly pseudocontraction. Under certain approximate conditions, the sequence {xn} converges strongly to x* ∈ ∪i=1∞F(Ti), which solves some variational inequality. The results here improve and extend some recent results. [ABSTRACT FROM AUTHOR]

The object of investigation of the paper is a special type of functional differential equations containing the maximum value of the unknown function over a past time interval. An improved algorithm of the monotone-iterative technique is suggested to nonlinear differential equations with "maxima." The case when upper and lower solutions of the given problem are known at different initial time is studied. Additionally, all initial value problems for successive approximations have both initial time and initial functions different. It allows us to construct sequences of successive approximations as well as sequences of initial functions, which are convergent to the solution and to the initial function of the given initial value problem, respectively. The suggested algorithm is realized as a computer program, and it is applied to several examples, illustrating the advantages of the suggested scheme. [ABSTRACT FROM AUTHOR]

Fixed point especially, the minimum norm fixed point computation is an interesting topic due to its practical applications in natural science. The purpose of the paper is devoted to finding the common fixed points of an infinite family of nonexpansive mappings. We introduce an iterative algorithm and prove that suggested scheme converges strongly to the common fixed points of an infinite family of nonexpansive mappings under some mild conditions. As a special case, we can find the minimum norm common fixed point of an infinite family of nonexpansive mappings. [ABSTRACT FROM AUTHOR]

Iterative methods for pseudocontractions have been studied by many authors in the literature. In the present paper, we firstly propose a new iterative method involving sunny nonexpansive retractions for pseudocontractions in Banach spaces. Consequently, we show that the suggested algorithm converges strongly to a fixed point of the pseudocontractive mapping which also solves some variational inequality. [ABSTRACT FROM AUTHOR]

In 2002, Dierk Schleicher gave an explicit estimate of an upper bound for the number of iterations of Newton's method it takes to find all roots of polynomials with prescribed precision. In this paper, we provide a method to improve the upper bound given by D. Schleicher. We give here an iterative method for finding an upper bound for the distance between a fixed point z in an immediate basin of a root α to α, which leads to a better upper bound for the number of iterations of Newton's method. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new H(·, ·)-cocoercive operator, which generalizes many existing monotone operators. The resolvent operator associated with H(·,·)-cocoercive operator is defined, and its Lipschitz continuity is presented. By using techniques of resolvent operator, a new iterative algorithm for solving generalized variational inclusions is constructed. Under some suitable conditions, we prove the convergence of iterative sequences generated by the algorithm. For illustration, some examples are given. [ABSTRACT FROM AUTHOR]