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In this paper, we introduce a proximal point algorithm for approximating a common solution of finite family of convex minimization problems and fixed point problems for k -demicontractive mappings in complete CAT(0) spaces. We prove a strong convergence result and obtain other consequence results which generalize and extend some recent results in the literature. We further provide a numerical example to illustrate the convergence behaviour of the sequence generated by our algorithm. [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 Bregman Proximal Gradient (BPG) algorithm is an algorithm for minimizing the sum of two convex functions, with one being nonsmooth. The supercoercivity of the objective function is necessary for the convergence of this algorithm precluding its use in many applications. In this paper, we give an inexact version of the BPG algorithm while circumventing the condition of supercoercivity by replacing it with a simple condition on the parameters of the problem. Our study covers the existing results, while giving other. [ABSTRACT FROM AUTHOR]

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]

A new reliable algorithm based on an adaptation of the standard generalized differential transform method (GDTM) is presented. The GDTM is treated as an algorithm in a sequence of intervals (i.e., time step) for finding accurate approximate solutions of fractional-order Rössler chaotic and hyperchaotic systems. A comparative study between the new algorithm and the classical Runge- Kutta method is presented in the case of integer-order derivatives. The algorithm described in this paper is expected to be further employed to solve similar nonlinear problems in fractional calculus. [ABSTRACT FROM AUTHOR]

The problem of learning the kernel function with linear combinations of multiple kernels has attracted considerable attention recently in machine learning. Specially, by imposing an lp-norm penalty on the kernel combination coefficient, multiple kernel learning (MKL) was proved useful and effective for theoretical analysis and practical applications (Kloft et al., 2009, 2011). In this paper, we present a theoretical analysis on the approximation error and learning ability of the lp norm MKL. Our analysis shows explicit learning rates for lp-norm MKL and demonstrates some notable advantages compared with traditional kernel-based learning algorithms where the kernel is fixed. [ABSTRACT FROM AUTHOR]

We construct a sequence of proximal iterates that converges strongly underminimal assumptions) to a common zero of two maximal monotone operators in a Hilbert space. The algorithm introduced in this paper puts together several proximal point algorithms under one frame work. Therefore, the results presented here generalize and improve many results related to the proximal point algorithm which were announced recently in the literature. [ABSTRACT FROM AUTHOR]

This paper applies an ancient Chinese algorithm to differential-difference equations, and a solitarysolution formulation is obtained. The discrete mKdV lattice equation is used as an example to elucidate the solution procedure [ABSTRACT FROM AUTHOR]

A new hybrid projection algorithm is considered for a ?-strict asymptotically pseudocontractive mapping. Using the metric projection, a strong convergence theorem is obtained in a uniformly convex and 2-uniformly smooth Banach spaces. The result presented in this paper mainly improves and extends the corresponding results of Matsushita and Takahashi (2008), Dehghan (2011) Kang and Wang (2011), and many others. [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]

We present an algorithm for C1 Hermite interpolation using Mobius transformations of planar polynomial Pythagoreanhodograph (PH) cubics. In general, with PH cubics, we cannot solve C1 Hermite interpolation problems, since their lack of parameters makes the problems overdeter-mined. In this paper, we show that, for each Mobius transformation, we can introduce an extra parameter determined by the transformation, with which we can reduce them to the problems determining PH cubics in the complex plane C. Mobius transformations preserve the PH property of PH curves and are biholomorphic. Thus the interpolants obtained by this algorithm are also PH and preserve the topology of PH cubics. We present a condition to be met by a Hermite dataset, in order for the corresponding interpolant to be simple or to be a loop. We demonstrate the improved stability of these new interpolants compared with PH quintics. [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]

This paper studies the adaptive fault estimation problems for stochastic Markovian jump systems (MJSs) with time delays. With the aid of the selected Lyapunov-Krasovskii functional, the adaptive fault estimation algorithm based on adaptive observer is proposed to enhance the rapidity and accuracy performance of fault estimation. A sufficient condition on the existence of adaptive observer is presented and proved by means of linear matrix inequalities techniques. The presented results are extended to multiple time-delayed MJSs. Simulation results illustrate that the validity of the proposed adaptive faults estimation algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a multiobjective differential evolution algorithm with multiple trial vectors. For each individual in the population, three trial individuals are produced by the mutation operator. The offspring is produced by using the crossover operator on the three trial individuals. Good individuals are selected from the parent and the offspring and then are put in the intermediate population. Finally, the intermediate population is sorted according to the Pareto dominance relations and the crowding distance, and then the outstanding individuals are selected as the next evolutionary population. Comparing with the classical multiobjective optimization algorithm NSGA-II, the proposed algorithm has better convergence, and the obtained Pareto optimal solutions have better diversity [ABSTRACT FROM AUTHOR]

The main purpose of this paper is by using a hybrid algorithm to find a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for variational inequality problems, and the set of common fixed points for a infinite family of total quasi-f- asymptotically nonexpansive multivalued mapping in a real uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in this paper improve and extend some recent results announced by some authors. [ABSTRACT FROM AUTHOR]

Many applied problems such as image reconstructions and signal processing can be formulated as the split feasibility problem (SFP). Some algorithms have been introduced in the literature for solving the (SFP). In this paper, we will continue to consider the convergence analysis of the regularized methods for the (SFP). Two regularized methods are presented in the present paper. Under some different control conditions, we prove that the suggested algorithms strongly converge to the minimum norm solution of the (SFP). [ABSTRACT FROM AUTHOR]

For the superreplication problem with discrete time, a guaranteed deterministic formulation is considered: the problem is to guarantee coverage of the contingent liability on sold option under all admissible scenarios. These scenarios are defined by means of a priori defined compacts dependent on price prehistory: the price increments at each point in time must lie in the corresponding compacts. In a general case, we consider a market with trading constraints and assume the absence of transaction costs. The formulation of the problem is game theoretic and leads to the Bellman–Isaacs equations. This paper analyses the solution to these equations for a specific pricing problem, i.e., for a binary option of the European type, within a multiplicative market model, with no trading constraints. A number of solution properties and an algorithm for the numerical solution of the Bellman equations are derived. The interest in this problem, from a mathematical prospective, is related to the discontinuity of the option payoff function. [ABSTRACT FROM AUTHOR]

In this paper, we study and modify the algorithm of Kraikaew and Saejung for the class of total quasi-asymptotically nonexpansive case so that the strong convergence is guaranteed for the solution of split common fixed-point problems in Hilbert space. Moreover, we justify our result through an example. The results presented in this paper not only extend the result of Kraikaew and Saejung but also extend, improve, and generalize some existing results in the literature. [ABSTRACT FROM AUTHOR]

This paper investigates robust simultaneous stabilization (RSS) control method for two port-controlled Hamiltonian (PCH) systems and proposes results on the design of simultaneous stabilization controller with parameters for such systems. Firstly, two PCH systems are studied. Using the dissipative Hamiltonian structural properties, the systems are combined to generate an augmented PCH system. When there are external disturbances in the systems, a robust controller with parameters is designed for the systems. Secondly, an algorithm for solving parameters of the controller is proposed with symbolic computation. Finally, an illustrative example is presented to show that the RSS controller obtained in this paper works very well. [ABSTRACT FROM AUTHOR]

In the era of big data, many urgent issues to tackle in all walks of life all can be solved via big data technique. Compared with the Internet, economy, industry, and aerospace fields, the application of big data in the area of architecture is relatively few. In this paper, on the basis of the actual data, the values of Boston suburb houses are forecast by several machine learning methods. According to the predictions, the government and developers can make decisions about whether developing the real estate on corresponding regions or not. In this paper, support vector machine (SVM), least squares support vector machine (LSSVM), and partial least squares (PLS)methods are used to forecast the home values. And these algorithms are compared according to the predicted results. Experiment shows that although the data set exists serious nonlinearity, the experiment result also show SVM and LSSVM methods are superior to PLS on dealing with the problem of nonlinearity. The global optimal solution can be found and best forecasting effect can be achieved by SVM because of solving a quadratic programming problem. In this paper, the different computation deficiencies of the algorithms are compared according to the computing times of relevant algorithms. [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]

This paper presents a tube-based model predictive control (MPC) algorithm with piecewise affine control laws for discrete-time linear systems in the presence of bounded disturbances. By solving the standard multiparametric quadratic programming (mp-QP), the explicit piecewise affine control laws for tube-based MPC are obtained. Each control law is piecewise affine with respect to the corresponding region (one of the partitions of the feasible set). Due to the fact that the above-mentioned procedures are totally offline, the online computation time is short enough for stabilizing those systems with fast dynamics. In this paper, all the involved constraint sets are assumed to be polytopes. An illustrative example is utilized to verify the feasibility and efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

For solving Laplace's equation in circular domains with circular holes, the null field method (NFM) was developed by Chen and his research group (see Chen and Shen (2009)). In Li et al. (2012) the explicit algebraic equations of the NFM were provided, where some stability analysis was made. For the NFM, the conservative schemes were proposed in Lee et al. (2013), and the algorithm singularity was fully investigated in Lee et al., submitted to Engineering Analysis with Boundary Elements, (2013). To target the same problems, a new interior field method (IFM) is also proposed. Besides the NFM and the IFM, the collocation Trefftz method (CTM) and the boundary integral equation method (BIE) are two effective boundary methods. This paper is devoted to a further study on NFM and IFM for three goals. The first goal is to explore their intrinsic relations. Since there exists no error analysis for the NFM, the second goal is to drive error bounds of the numerical solutions. The third goal is to apply those methods to Laplace's equation in the domains with extremely small holes, which are called actually punctured disks. By NFM, IFM, BIE, and CTM, numerical experiments are carried out, and comparisons are provided. This paper provides an in-depth overview of four methods, the error analysis of the NFM, and the intriguing computation, which are essential for the boundary methods. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to deal with the shared set and uniqueness of meromorphic functions on annulus. The set of this paper is different from the set of the paper by Cao and Deng, and our theorems are improvement of the results given by Cao and Deng. [ABSTRACT FROM AUTHOR]

This paper investigates the consensus problem for second-order leader-follower nonlinearmultiagent systems with general network topologies. A pinning control algorithmis proposed, where it includes time-varying delay information. By using the information of delay-partition and delay-distribution and constructing an appropriate Lyapunov-Krasovskii functional, the consensus criteria are derived to achieve leader-follower consensus for multiagent systems, which are in the form of linear inequalities that can be solved by employing the semidefinite programme method. Moreover, this paper addresses what kind of agents and how many agents should be pinned. Two numerical examples are presented to further demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper considers the problem of the convergence of the consensus algorithm for multiple agents in a directed network where each agent is governed by double-integrator dynamics and coupling time delay. The advantage of this protocol is that almost all the existing linear local interaction consensus protocols can be considered as special cases of the present paper. By combining algebraic graph theory and matrix theory and studying the distribution of the eigenvalues of the associated characteristic equation, some necessary and sufficient conditions are derived for reaching the second-order consensus. Finally, an illustrative example is also given to support the theoretical results. [ABSTRACT FROM AUTHOR]

The first author of the above-mentioned paper regrets that the paper was published with the wrong address. The corrected address of the first author is given as above. [ABSTRACT FROM AUTHOR]

To overcome the staircasing effects introduced by the TV regularization in image restoration, this paper investigates a fourth-order partial differential equation PDE filter for removing Poisson noise. In consideration of the slow convergence property of the classical gradient descent method, we adopt the alternating minimization algorithm for realizing this scheme. Compared with the corresponding total variation based one, numerical simulations distinctly indicate the superiority of our proposed strategy in handling smooth regions of Poissonian images and improving the computational speed. [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]

This paper discusses the monotone variational inequality over the solution set of the variational inequality problem and the fixed point set of a nonexpansive mapping. The strong convergence theorem for the proposed algorithm to the solution is guaranteed under some suitable assumptions. [ABSTRACT FROM AUTHOR]

The gradient projection algorithm plays an important role in solving constrained convex minimization problems. In general, the gradient projection algorithm has only weak convergence in infinite-dimensional Hilbert spaces. Recently, H. K. Xu (2011) provided two modified gradient projection algorithms which have strong convergence. Motivated by Xu's work, in the present paper, we suggest three more simpler variant gradient projection methods so that strong convergence is guaranteed. [ABSTRACT FROM AUTHOR]

We introduce an algorithm for solving the split common fixed point problem for quasi-total asymptotically nonexpansive uniformly Lipschitzian mapping in Hilbert spaces. The results presented in this paper improve and extend some recent corresponding results. [ABSTRACT FROM AUTHOR]

This paper further studies the moment stability of pulse-width-modulated (PWM) feedback system which is subjected to multiplicative and additive random disturbance modeled by the derivative of Wiener process. Different from the existing investigation, we focus on its critical case. The linear plant considered herein is assumed to be critically stable; that is, the plant has one and only one pole at the origin, and the rest of the poles are left half of complex plane. We establish several globally asymptotically stability criteria for such PWM feedback systems and then propose an algorithm to calculate the stability bound effectively. Furthermore, we present two numerical examples to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents some efficient spectral algorithms for solving linear sixth-order two-point boundary value problems in one dimension based on the application of the Galerkin method. The proposed algorithms are extended to solve the two-dimensional sixth-order differential equations. A family of symmetric generalized Jacobi polynomials is introduced and used as basic functions. The algorithms lead to linear systems with specially structured matrices that can be efficiently inverted. The various matrix systems resulting from the proposed algorithms are carefully investigated, especially their condition numbers and their complexities. These algorithms are extensions to some of the algorithms proposed by Doha and Abd-Elhameed (2002) and Doha and Bhrawy (2008) for second- and fourth-order elliptic equations, respectively. Three numerical results are presented to demonstrate the efficiency and the applicability of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Obtaining periodic orbits of dynamical systems is the main source of information about how the orbits, in general, are organized. In this paper, we extend classical continuation algorithms in order to be able to obtain families of periodic orbits with high-precision. These periodic orbits can be corrected to get them with arbitrary precision. We illustrate the method with two important classical Hamiltonian problems. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to construct an implicit algorithm for finding the common solution of maximal monotone operators and strictly pseudocontractive mappings in Hilbert spaces. Some applications are also included. [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]

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]

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]

This paper introduces multiresolution analyses with composite dilations (AB-MRAs) and addresses frame multiresolution analyses with composite dilations in the setting of reducing subspaces of L²(ℝn) (AB-RMRAs). We prove that an AB-MRA can induce an AB-RMRA on a given reducing subspace L²(S)V. For a general expansive matrix, we obtain the characterizations for a scaling function to generate an AB-RMRA, and the main theorems generalize the classical results. Finally, some examples are provided to illustrate the general theory. [ABSTRACT FROM AUTHOR]

This paper is concerned with a generalization of the q-Bernstein polynomials and Stancu operators, where the function is evaluated at intervals which are in geometric progression. It is shown that these polynomials can be generated by a de Casteljau algorithm, which is a generalization of that relating to the classical case and q-Bernstein case. [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]

Bacterial Foraging Optimization (BFO) is a recently developed nature-inspired optimization algorithm, which is based on the foraging behavior of E. coli bacteria. Up to now, BFO has been applied successfully to some engineering problems due to its simplicity and ease of implementation. However, BFO possesses a poor convergence behavior over complex optimization problems as compared to other nature-inspired optimization techniques. This paper first analyzes how the run-length unit parameter of BFO controls the exploration of the whole search space and the exploitation of the promising areas. Then it presents a variation on the original BFO, called the adaptive bacterial foraging optimization (ABFO), employing the adaptive foraging strategies to improve the performance of the original BFO. This improvement is achieved by enabling the bacterial foraging algorithm to adjust the run-length unit parameter dynamically during algorithm execution in order to balance the exploration/exploitation tradeoff. The experiments compare the performance of two versions of ABFO with the original BFO, the standard particle swarm optimization (PSO) and a real-coded genetic algorithm (GA) on four widely-used benchmark functions. The proposed ABFO shows a marked improvement in performance over the original BFO and appears to be comparable with the PSO and GA. [ABSTRACT FROM AUTHOR]

We prove strong and weak convergence theorems for a new resolvent of maximal monotone operators in a Banach space and give an estimate of the convergence rate of the algorithm. Finally, we apply our convergence theorem to the convex minimization problem. The result present in this paper extend and improve the corresponding result of Ibaraki and Takahashi (2007), and Kim and Xu (2005). [ABSTRACT FROM AUTHOR]

We consider a hybrid projection algorithm based on the shrinking projection method for two families of quasi-f-nonexpansive mappings. We establish strong convergence theorems for approximating the common element of the set of the common fixed points of such two families and the set of solutions of the variational inequality for an inverse-strongly monotone operator in the framework of Banach spaces. As applications, at the end of the paper we first apply our results to consider the problem of finding a zero point of an inverse-strongly monotone operator and we finally utilize our results to study the problem of finding a solution of the complementarity problem. Our results improve and extend the corresponding results announced by recent results. [ABSTRACT FROM AUTHOR]

We introduce and study a new hybrid projection algorithm for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed points of relatively quasinonexpansive mappings, and the set of solutions of the variational inequality for an inversestrongly- monotone operator in a Banach space. Under suitable assumptions, we show a strong convergence theorem. Using this result,we obtain some applications in a Banach space. The results obtained in this paper extend and improve the several recent results in this area. [ABSTRACT FROM AUTHOR]