Takahashi's Legacy in Fixed Point Theory

Citation: Fixed Point Theory and Applications 2011 2010:721648

Remarks on Recent Fixed Point Theorems
Coincidence and fixed point theorems for a new class of contractive, nonexpansive and hybrid contractions are proved. Applications regarding the existence of common solutions of certain functional equations ar...
Citation: Fixed Point Theory and Applications 2010 2010:452905 
Fixed Point Properties Related to Multivalued Mappings
We discuss fixed point properties of convex subsets of locally convex linear topological spaces. We derive equivalence among fixed point properties concerning several types of multivalued mappings.
Citation: Fixed Point Theory and Applications 2010 2010:581728 
On Uniformly Generalized Lipschitzian Mappings
We consider another class of generalized Lipschitzian type mappings and utilize the same to prove fixed point theorems for asymptotically regular and uniformly generalized Lipschitzian oneparameter semigroups...
Citation: Fixed Point Theory and Applications 2010 2010:692401 
ContractiveLike Mapping Principles in Ordered Metric Spaces and Application to Ordinary Differential Equations
The purpose of this paper is to present a fixed point theorem for generalized contractions in partially ordered complete metric spaces. We also present an application to firstorder ordinary differential equat...
Citation: Fixed Point Theory and Applications 2010 2010:916064 
Maximality Principle and General Results of Ekeland and Caristi Types without Lower Semicontinuity Assumptions in Cone Uniform Spaces with Generalized Pseudodistances
Our aim is twofold: first, we want to introduce a partial quasiordering in cone uniform spaces with generalized pseudodistances for giving the general maximality principle in these spaces. Second, we want to s...
Citation: Fixed Point Theory and Applications 2010 2010:175453 
Generalizations of the Nash Equilibrium Theorem in the KKM Theory
The partial KKM principle for an abstract convex space is an abstract form of the classical KKM theorem. In this paper, we derive generalized forms of the Ky Fan minimax inequality, the von NeumannSion minima...
Citation: Fixed Point Theory and Applications 2010 2010:234706 
Fixed Point Iterations of a Pair of Hemirelatively Nonexpansive Mappings
We introduce an iterative method for a pair of hemirelatively nonexpansive mappings. Strong convergence of the purposed iterative method is obtained in a Banach space.
Citation: Fixed Point Theory and Applications 2010 2010:270150 
Coupled Fixed Point Theorems for Nonlinear Contractions Satisfied MizoguchiTakahashi's Condition in Quasiordered Metric Spaces
The main aim of this paper is to study and establish some new coupled fixed point theorems for nonlinear contractive maps that satisfied MizoguchiTakahashi's condition in the setting of quasiordered metric sp...
Citation: Fixed Point Theory and Applications 2010 2010:876372 
Convergence Theorems on Asymptotically Pseudocontractive Mappings in the Intermediate Sense
A new nonlinear mapping is introduced. The convergence of Ishikawa iterative processes for the class of asymptotically pseudocontractive mappings in the intermediate sense is studied. Weak convergence theorems...
Citation: Fixed Point Theory and Applications 2010 2010:186874 
A Version of Hilbert's 13th Problem for Infinitely Differentiable Functions
In 1957, Kolmogorov and Arnold gave a solution to the 13th problem which had been formulated by Hilbert in 1900. Actually, it is known that there exist many open problems which can be derived from the original...
Citation: Fixed Point Theory and Applications 2010 2010:287647 
On the FixedPoint Set of a Family of Relatively Nonexpansive and Generalized Nonexpansive Mappings
We prove that the set of common fixed points of a given countable family of relatively nonexpansive mappings is identical to the fixedpoint set of a single strongly relatively nonexpansive mapping. This answe...
Citation: Fixed Point Theory and Applications 2010 2010:414232 
Existence of Fixed Points of Firmly NonexpansiveLike Mappings in Banach Spaces
The aim of this paper is to obtain some existence theorems related to a hybrid projection method and a hybrid shrinking projection method for firmly nonexpansivelike mappings (mappings of type (P)) in a Banac...
Citation: Fixed Point Theory and Applications 2010 2010:512751 
Fixed Point Results for Multivalued Maps in Metric Spaces with Generalized Inwardness Conditions
We establish fixed point theorems for multivalued mappings defined on a closed subset of a complete metric space. We generalize Lim's result on weakly inward contractions in a Banach space. We also generalize ...
Citation: Fixed Point Theory and Applications 2010 2010:183217 
Strong Convergence of Iterative Schemes for Zeros of Accretive Operators in Reflexive Banach Spaces
We introduce composite iterative schemes by the viscosity iteration method for finding a zero of an accretive operator in reflexive Banach spaces. Then, under certain differen control conditions, we establish ...
Citation: Fixed Point Theory and Applications 2010 2010:103465 
New Hybrid Iterative Schemes for an Infinite Family of Nonexpansive Mappings in Hilbert Spaces
We propose some new iterative schemes for finding common fixed point of an infinite family of nonexpansive mappings in a Hilbert space and prove the strong convergence of the proposed schemes. Our results exte...
Citation: Fixed Point Theory and Applications 2010 2010:572838 
Existence and Approximation of Fixed Points for SetValued Mappings
Taking into account possibly inexact data, we study both existence and approximation of fixed points for certain setvalued mappings of contractive type. More precisely, we study the existence of convergent it...
Citation: Fixed Point Theory and Applications 2010 2010:351531 
The Szlenk Index and the Fixed Point Property under Renorming
Assume that is a Banach space such that its Szlenk index i...
Citation: Fixed Point Theory and Applications 2010 2010:268270 
Iterative Algorithms with Variable Coefficients for Asymptotically Strict Pseudocontractions
We introduce and study some new CQtype iterative algorithms with variable coefficients for asymptotically strict pseudocontractions in real Hilbert spaces. General results for asymptotically strict pseudocont...
Citation: Fixed Point Theory and Applications 2010 2010:948529 
Hybrid SteepestDescent Methods for Solving Variational Inequalities Governed by Boundedly Lipschitzian and Strongly Monotone Operators
Let be a real Hilbert space and let be a boundedly Lipschi...
Citation: Fixed Point Theory and Applications 2010 2010:673932 
Fixed Point Theorem of HalfContinuous Mappings on Topological Vector Spaces
Some fixed point theorems of halfcontinuous mappings which are possibly discontinuous defined on topological vector spaces are presented. The results generalize the work of Philippe Bich (2006) and several we...
Citation: Fixed Point Theory and Applications 2010 2010:814970 
Strong and Weak Convergence Theorems for Common Solutions of Generalized Equilibrium Problems and Zeros of Maximal Monotone Operators
The purpose of this paper is to introduce and study two modified hybrid proximalpoint algorithms for finding a common element of the solution set EP of a generalized equilibrium problem and the set
Citation: Fixed Point Theory and Applications 2010 2010:590278 
On the Convergence for an Iterative Method for Quasivariational Inclusions
We introduce an iterative algorithm for finding a common element of the set of solutions of quasivariational inclusion problems and of the set of fixed points of strict pseudocontractions in the framework Hilb...
Citation: Fixed Point Theory and Applications 2010 2010:278973 
Strong and Weak Convergence of the Modified Proximal Point Algorithms in Hilbert Space
For a monotone operator , we shall show weak convergence of Rockafellar's proximal point algorithm to some zero of ...
Citation: Fixed Point Theory and Applications 2010 2010:240450 
Convergence Theorems for the Unique Common Fixed Point of a Pair of Asymptotically Nonexpansive Mappings in Generalized Convex Metric Space
Let be a generalized convex metric space, and let ,
Citation: Fixed Point Theory and Applications 2010 2010:281890 
Hybrid Methods for Equilibrium Problems and Fixed Points Problems of a Countable Family of Relatively Nonexpansive Mappings in Banach Spaces
The purpose of this paper is to introduce hybrid projection algorithms for finding a common element of the set of common fixed points of a countable family of relatively nonexpansive mappings and the set of so...
Citation: Fixed Point Theory and Applications 2009 2010:962628 
Approximation of Common Fixed Points of a Countable Family of Relatively Nonexpansive Mappings
We introduce two general iterative schemes for finding a common fixed point of a countable family of relatively nonexpansive mappings in a Banach space. Under suitable setting, we not only obtain several conve...
Citation: Fixed Point Theory and Applications 2009 2010:407651 
On Two Iterative Methods for Mixed Monotone Variational Inequalities
A mixed monotone variational inequality (MMVI) problem in a Hilbert space is formulated to find a point ...
Citation: Fixed Point Theory and Applications 2009 2010:291851 
Approximating Fixed Points of Nonexpansive Nonself Mappings in CAT(0) Spaces
Suppose that is a nonempty closed convex subset of a complete CAT(0) space
Citation: Fixed Point Theory and Applications 2009 2010:367274 
TraceInequalities and MatrixConvex Functions
A realvalued continuous function on an interval gives ris...
Citation: Fixed Point Theory and Applications 2009 2010:241908 
Convergence Theorems of Modified Ishikawa Iterative Scheme for Two Nonexpansive Semigroups
We prove convergence theorems of modified Ishikawa iterative sequence for two nonexpansive semigroups in Hilbert spaces by the two hybrid methods. Our results improve and extend the corresponding results annou...
Citation: Fixed Point Theory and Applications 2009 2010:914702 
Strong Convergence Theorems of Common Fixed Points for a Family of Quasi Nonexpansive Mappings
We consider a modified Halpern type iterative algorithm for a family of quasi nonexpansive mappings in the framework of Banach spaces. Strong c...
Citation: Fixed Point Theory and Applications 2009 2010:754320 
Common Fixed Points for Multimaps in Metric Spaces
We discuss the existence of common fixed points in uniformly convex metric spaces for singlevalued pointwise asymptotically nonexpansive or nonexpansive mappings and multivalued nonexpansive, ...
Citation: Fixed Point Theory and Applications 2009 2010:204981 
Some Characterizations for a Family of Nonexpansive Mappings and Convergence of a Generated Sequence to Their Common Fixed Point
Motivated by the method of Xu (2006) and Matsushita and Takahashi (2008), we characterize the set of all common fixed points of a family of nonexpansive mappings by the notion of Mosco convergence and prove st...
Citation: Fixed Point Theory and Applications 2009 2010:732872