Citation: Fixed Point Theory and Applications 2014 2014:122
Variational Analysis and Fixed Point Theory
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Fixed point theorems for monotone multivalued mappings in partially ordered metric spaces
In this paper, we introduce two new types of monotone multivalued mappings in partially ordered metric spaces and prove some fixed point theorems of those two types of mappings under some contraction conditio...
Citation: Fixed Point Theory and Applications 2014 2014:110

The relationship between multiobjective robustness concepts and setvalued optimization
In this paper, we discuss the connection between concepts of robustness for multiobjective optimization problems and set order relations. We extend some of the existing concepts to general spaces and cones us...
Citation: Fixed Point Theory and Applications 2014 2014:83

General iterative algorithms for mixed equilibrium problems, variational inequalities and fixed point problems
In this paper, we introduce and analyze a general iterative algorithm for finding a common solution of a mixed equilibrium problem, a general system of variational inequalities and a fixed point problem of inf...
Citation: Fixed Point Theory and Applications 2014 2014:80

A class of nonlinear mixed ordered inclusion problems for ordered $({\alpha}_{A},\lambda )$ANODM setvalued mappings with strong comparison mapping A
The purpose of this paper is to introduce and study a new class of nonlinear mixed ordered inclusion problems in ordered Banach spaces and to obtain an existence theorem and a comparability theorem of the reso...
Citation: Fixed Point Theory and Applications 2014 2014:79

Iterative methods for the split common fixed point problem in Hilbert spaces
The split common fixed point problem is an inverse problem that consists in finding an element in a fixed point set such that its image under a bounded linear operator belongs to another fixed point set. Recen...
Citation: Fixed Point Theory and Applications 2014 2014:78

Strong and weak convergence theorems for common zeros of finite accretive mappings
In this paper, we present a new iterative scheme to solve the problems of finding common zeros of finite maccretive mappings in a real Hilbert space. Some strong and weak convergence theorems are established und...
Citation: Fixed Point Theory and Applications 2014 2014:77

Fixed point approximation of asymptotically nonexpansive mappings in hyperbolic spaces
Convergence theorems are established in a hyperbolic space for the modified Noor iterations with errors of asymptotically nonexpansive mappings. The obtained results extend and improve the several known result...
Citation: Fixed Point Theory and Applications 2014 2014:64

Coupled coincidence point results for a generalized compatible pair with applications
In this paper, employing a new concept of generalized compatibility of a pair of mappings defined on a product space, certain coupled coincidence point results of mappings involved herein are obtained. We also...
Citation: Fixed Point Theory and Applications 2014 2014:62

Mosco convergence results for common fixed point problems and generalized equilibrium problems in Banach spaces
In this paper, we propose and analyze an explicit type algorithm for finding a common element of the set of solutions of a finite family of generalized equilibrium problems and the set of common fixed points o...
Citation: Fixed Point Theory and Applications 2014 2014:59

Approximate solutions to variational inequality over the fixed point set of a strongly nonexpansive mapping
Variational inequality problems over fixed point sets of nonexpansive mappings include many practical problems in engineering and applied mathematics, and a number of iterative methods have been presented to s...
Citation: Fixed Point Theory and Applications 2014 2014:51

Best proximity point theorems for weakly contractive mapping and weakly Kannan mapping in partial metric spaces
The purpose of this paper is to obtain best proximity point theorems for a weakly contractive mapping and a weakly Kannan mapping in partial metric spaces. In this paper, the Poperator technique, which changes a...
Citation: Fixed Point Theory and Applications 2014 2014:50

Fixed point theorems for a new nonlinear mapping similar to a nonspreading mapping
We introduce a new nonlinear mapping similar to the nonspreading mapping which is defined by Kohsaka and Takahashi (Arch. Math. 91:166177, 2008). We prove fixed point theorems for such a mapping without the c...
Citation: Fixed Point Theory and Applications 2014 2014:47

Citation: Fixed Point Theory and Applications 2014 2014:44

A fixed point theorem for generalized contractions involving wdistances on complete quasimetric spaces
We obtain a fixed point theorem for generalized contractions on complete quasimetric spaces, which involves wdistances and functions of MeirKeeler and Jachymski type. Our result generalizes in various directio...
Citation: Fixed Point Theory and Applications 2014 2014:40

General split equality problems in Hilbert spaces
A new convex feasibility problem, the split equality problem (SEP), has been proposed by Moudafi and Byrne. The SEP was solved through the ACQA and ARCQA algorithms. In this paper the SEPs are extended to infi...
Citation: Fixed Point Theory and Applications 2014 2014:35

Approximating fixed points of multivalued ρnonexpansive mappings in modular function spaces
The existence of fixed points of singlevalued mappings in modular function spaces has been studied by many authors. The approximation of fixed points in such spaces via convergence of an iterative process for...
Citation: Fixed Point Theory and Applications 2014 2014:34

Convergence theorems for some multivalued generalized nonexpansive mappings
In this paper, we propose an algorithms for finding a common fixed point of an infinite family of multivalued generalized nonexpansive mappings in uniformly convex Banach spaces. Under suitable conditions some s...
Citation: Fixed Point Theory and Applications 2014 2014:33

Relaxed and composite viscosity methods for variational inequalities, fixed points of nonexpansive mappings and zeros of accretive operators
In this paper, we present relaxed and composite viscosity methods for computing a common solution of a general systems of variational inequalities, common fixed points of infinitely many nonexpansive mappings ...
Citation: Fixed Point Theory and Applications 2014 2014:29

A note on spherical maxima sharing the same Lagrange multiplier
In this paper, we establish a general result on spherical maxima sharing the same Lagrange multiplier of which the following is a particular consequence: Let X be a real Hilbert space. For each
Citation: Fixed Point Theory and Applications 2014 2014:25

Common fixedpoint results for generalized Berindetype contractions which involve altering distance functions
In this paper, the existence and the uniqueness of a common fixed point for two selfmappings satisfying some generalized Berindetype contractions which involve an altering distance function with
Citation: Fixed Point Theory and Applications 2014 2014:24

A modified projection method for a common solution of a system of variational inequalities, a split equilibrium problem and a hierarchical fixedpoint problem
In this paper, we suggest and analyze a modified projection method for finding a common solution of a system of variational inequalities, a split equilibrium problem, and a hierarchical fixedpoint problem in ...
Citation: Fixed Point Theory and Applications 2014 2014:22

Mathematical programming with multiple sets split monotone variational inclusion constraints
In this paper, we first study a hierarchical problem of Baillon’s type, and we study a strong convergence theorem of this problem. For the special case of this convergence theorem, we obtain a strong convergen...
Citation: Fixed Point Theory and Applications 2014 2014:20

Viscosity approximation process for a sequence of quasinonexpansive mappings
We study the viscosity approximation method due to Moudafi for a fixed point problem of quasinonexpansive mappings in a Hilbert space. First, we establish a strong convergence theorem for a sequence of quasino...
Citation: Fixed Point Theory and Applications 2014 2014:17

Iterative algorithms based on hybrid method and Cesàro mean of asymptotically nonexpansive mappings for equilibrium problems
Using Cesàro means of a mapping, we modify the progress of Mann’s iteration in hybrid method for asymptotically nonexpansive mappings in Hilbert spaces. Under suitable conditions, we prove that the iterative s...
Citation: Fixed Point Theory and Applications 2014 2014:16

Weak and strongconvergence theorems of solutions to split feasibility problem for nonspreading type mapping in Hilbert spaces
The purpose of this article is to study the weak and strongconvergence theorems of solutions to split a feasibility problem for a family of nonspreadingtype mapping in Hilbert spaces. The main result presen...
Citation: Fixed Point Theory and Applications 2014 2014:11

Several types of wellposedness for generalized vector quasiequilibrium problems with their relations
The conceptions of (generalized) Tykhonov wellposedness for generalized vector quasiequilibrium problems, (generalized) Hadamard wellposedness for parametrically generalized vector quasiequilibrium problem...
Citation: Fixed Point Theory and Applications 2014 2014:8

Citation: Fixed Point Theory and Applications 2014 2014:7

Fixed point results for modified weak and rational αψcontractions in ordered 2metric spaces
We first introduce the concept of a triangular 2αηadmissible mapping which extends the notion of αadmissible mapping with respect to η to 2metric spaces. Next, we introduce the concepts of modified weak and ...
Citation: Fixed Point Theory and Applications 2014 2014:6

On the Ishikawa iteration processes for multivalued mappings in some $CAT(\kappa )$ spaces
The purpose of this paper is to prove the strong convergence of the Ishikawa iteration processes for some generalized multivalued nonexpansive mappings in the framework of CAT(1) spaces. Our results extend the...
Citation: Fixed Point Theory and Applications 2014 2014:1

Strong convergence theorems for the split variational inclusion problem in Hilbert spaces
In this paper, we first consider a split variational inclusion problem and give several strong convergence theorems in Hilbert spaces, like the HalpernMann type iteration method and the regularized iteration ...
Citation: Fixed Point Theory and Applications 2013 2013:350

Citation: Fixed Point Theory and Applications 2013 2013:349

Fixed point theorems for a class of nonlinear operators in Hilbert spaces with lattice structure and application
We discuss the existence of a fixed point for a class of nonlinear operators in Hilbert spaces with lattice structure by a combination of variational and partial ordered methods. An application to secondorder...
Citation: Fixed Point Theory and Applications 2013 2013:345

Convergence results for a common solution of a finite family of variational inequality problems for monotone mappings with Bregman distance function
In this paper, we introduce an iterative process which converges strongly to a common solution of a finite family of variational inequality problems for monotone mappings with Bregman distance function. Our co...
Citation: Fixed Point Theory and Applications 2013 2013:343

Existence theorems of an extension for generalized strong vector quasiequilibrium problems
In this paper, we study generalized strong vector quasiequilibrium problems in topological vector spaces. Using the generalization of FanBrowder fixed point theorem, we provide existence theorems for an exte...
Citation: Fixed Point Theory and Applications 2013 2013:342

On generalized FenchelMoreau theorem and secondorder characterization for convex vector functions
Based on the concept of conjugate and biconjugate maps introduced in (Tan and Tinh in Acta Math. Viet. 25:315345, 2000) we establish a full generalization of the FenchelMoreau theorem for the vector case. Be...
Citation: Fixed Point Theory and Applications 2013 2013:328

On sequences of fuzzy sets and fuzzy setvalued mappings
Based on level sets of fuzzy sets, we propose definitions of limits of sequences of fuzzy sets, and limits and derivatives of fuzzy setvalued mappings. Then, their properties are derived. Limits of sequences ...
Citation: Fixed Point Theory and Applications 2013 2013:327

A new hybrid iteration method for a finite family of asymptotically nonexpansive mappings in Banach spaces
In this paper, we first introduce a new hybrid iteration method for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces, and then we discuss the strong and weak c...
Citation: Fixed Point Theory and Applications 2013 2013:322

Variational relation problems: existence of solutions and fixed points of contraction mappings
We propose a new approach to study variational relation problems. Namely, we apply Mizoguchi and Takahashi’s fixed point theorem of contraction mappings and an error bound of a system of linear inequalities to...
Citation: Fixed Point Theory and Applications 2013 2013:315

Hybrid iterative algorithms for nonexpansive and nonspreading mappings in Hilbert spaces
Recently, Iemoto and Takahashi considered a weak convergence iterative scheme for a nonspreading mapping and a nonexpansive mapping in Hilbert spaces. In this paper, we suggest two hybrid iterative algorithms ...
Citation: Fixed Point Theory and Applications 2013 2013:314

Citation: Fixed Point Theory and Applications 2013 2013:304

Iterative methods for hierarchical common fixed point problems and variationalinequalities
The purpose of this paper is to deal with the problem of finding hierarchically acommon fixed point of a sequence of nearly nonexpansive selfmappings defined ona closed convex subset of a real Hilbert space w...
Citation: Fixed Point Theory and Applications 2013 2013:299

Strong convergence theorem for total quasiϕasymptotically nonexpansive mappings in a Banach space
In this paper, we prove strong convergence theorems to a point which is a fixed point of multivalued mappings, a zero of an αinversestrongly monotone operator and a solution of the equilibrium problem. Next, w...
Citation: Fixed Point Theory and Applications 2013 2013:297

Convergence criteria of Newton’s method on Lie groups
In the present paper, we study Newton’s method on Lie groups (independent of affine connections) for finding zeros of a mapping f from a Lie group to its Lie algebra. Under a generalized Laverage Lipschitz condi...
Citation: Fixed Point Theory and Applications 2013 2013:293

Iterative algorithms with regularization for hierarchical variational inequality problems and convex minimization problems
In this paper, we consider a variational inequality problem which is defined over the set of intersections of the set of fixed points of a ζstrictly pseudocontractive mapping, the set of fixed points of a nonexp...
Citation: Fixed Point Theory and Applications 2013 2013:284

Citation: Fixed Point Theory and Applications 2013 2013:281

Iterative algorithms for monotone inclusion problems, fixed point problems and minimization problems
We introduce new implicit and explicit iterative schemes for finding a common element of the set of fixed points of kstrictly pseudocontractive mapping and the set of zeros of the sum of two monotone operators i...
Citation: Fixed Point Theory and Applications 2013 2013:272

Total Lagrange duality for DC infinite optimization problems
We present some total Lagrange duality results for inequality systems involving infinitely many DC functions. By using properties of the subdifferentials of involved functions, we introduce some new notions of...
Citation: Fixed Point Theory and Applications 2013 2013:269

Iteration scheme for common fixed points of hemicontractive and nonexpansive operators in Banach spaces
The purpose of this paper is to characterize the conditions for the convergence of the iterative scheme in the sense of Agarwal et al. (J. Nonlinear Convex. Anal. 8(1): 6179, 2007), associated with nonexpansive ...
Citation: Fixed Point Theory and Applications 2013 2013:247

Best proximity points and extension of MizoguchiTakahashi’s fixed point theorems
In this paper, we introduce a multivalued cyclic generalized contraction by extending the Mizoguchi and Takahashi’s contraction for nonself mappings. We also establish a best proximity point for such type co...
Citation: Fixed Point Theory and Applications 2013 2013:242