Unique Common Fixed Points for Two Weakly C~*-contractive Mappings on Partially Ordered 2-metric Spaces

In this paper, we give existence theorems of common fixed points for two mappings with a weakly C?-contractive condition on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point.     

Unique Common Fixed Point for a Family of Mappings with a Nonlinear Quasi-Contractive Type Condition in Metrically Convex Spaces

A class Φ of 5-dimensional functions was introduced and an existence and uniqueness of common fixed points for a family of non-self mappings satisfying a φiquasi-contractive condition and a certain boundary condition was given on complete metrically convex metric spaces, and from which, more general unique common fixed point theorems were obtained. Our main results generalize and improve many same type common fixed point theorems in references.     

WEAK CONVERGENCE THEOREMS FOR GENERAL EQUILIBRIUM PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS IN BANACH SPACES

In this paper,we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-strongly monotone operator and the set of common fixed points of two infinite families of relatively nonexpansive mappings or the set of common fixed points of an infinite family of relatively quasi-nonexpansive mappings in Banach spaces.Then we study the weak convergence of the two iterative sequences.Our results improve and extend the results announced by many others.     

Viscosity iterative methods for common fixed points of two nonexpansive mappings without commutativity assumption in Hilbert spaces

In this article, we introduce a new viscosity iterative method for two nonexpansive mappings in Hilbert spaces. We also prove, without commutativity assumption, that the iterates converge to a common fixed point of the mappings which solves some variational inequality. The results presented extend the corresponding results of Shimizu and Takahashi [T. Shimizu, W. Takahashi, Strong convergence to common fixed point of families of nonexpansive mappings, J. Math. Anal. Appl. 211 (1997), 71-83], and Yao and Chen [Y. Yao, R. Chen, Convergence to common fixed points of average mappings without commutativity assumption in Hilbert spaces, Nonlinear Analysis 67(2007), 1758-1763].     

Common Fixed Points for a Countable Family of Quasi-Contractive Mappings on a Cone Metric Space with the Convex Structure

In this paper, we consider a countable family of surjective mappings {Tn}n∈N satisfying certain quasi-contractive conditions. We also construct a convergent sequence { Xn } n c∈Nby the quasi-contractive conditions of { Tn } n ∈N and the boundary condition of a given complete and closed subset of a cone metric space X with convex structure, and then prove that the unique limit x＂ of {xn}n∈N is the unique common fixed point of {Tn}n∈N. Finally, we will give more generalized common fixed point theorem for mappings {Ti,j}i,j∈N. The main theorems in this paper generalize and improve many known common fixed point theorems for a finite or countable family of mappings with quasi-contractive conditions.     

On Positive Eigenvalues and Positive Fixed Points of Multivalued Condensing Mappings

In this paper,we discuss the calculations of fixed point indexs for multivalued condensing mappings and k-set-contraction mappings,obtain some theorems on the eigenvalues and the fixed points under the suitable conditions. Our conclusions improve and generalize some well-known results.     

APPROXIMATING COMMON FIXED POINTS OF NEARLY ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

We use an iteration scheme to approximate common fixed points of nearly asymptotically nonexpansive mappings.We generalize corresponding theorems of [1] to the case of two nearly asymptotically nonexpansive mappings and those of [9] not only to a larger class of mappings but also with better rate of convergence.     

Common Fixed Points for Mappings with Quasi-Lipschitz Conditions on TVS-valued Cone Metric Spaces

A new unique common fixed point result for a pair of mappings satisfying certain quasi-Lipschitz type conditions on a topological vector space-valued cone metric space is obtained, and its particular forms and a more general form are given. Our main results generalize and improve some well-known recent results in the literature.     

Fixed Points of Mappings Satisfying a Weakly Contractive Type Condition

In this paper, we discuss a fixed point theorem for mappings derived by a pair of mappings satisfying weak(k, k/) contractive type condition on the tensor product spaces. Let X and Y be Banach spaces and T_1 : X γ Y → X and T_2: X γ Y → Y be two operators which satisfy weak(k, k/) contractive type condition. Using T_1 and T_2, we construct an operator T on X γ Y and show that T has a unique fixed point in a closed and bounded subset of X γ Y.We derive an iteration scheme converging to this unique fixed point of T. Conversely, using a weakly contractive mapping T, we construct a pair of mappings(T_1, T_2) satisfying weak(k, k/)contractive type condition on X γ Y and from this pair, we also obtain two self mappings S_1 and S_2 on X and Y respectively with unique fixed points.     

Common Fixed Point Theorems and Q-prop erty for Quasi-contractive Mappings under c-distance on TVS-valued Cone Metric Spaces without the Normality

Fixed point and common fixed point results for mappings satisfying quasi-contractive conditions expressed in the terms of c-distance on TVS-valued cone met-ric spaces (without the underlying cone which is not normal) are obtained, and P-property and Q-property for mappings in the terms of c-distance are discussed. Our results generalize and improve many known results.     

Common Fixed Points for a Countable Family of Non-self Mappings in Cone Metric Spaces with the Convex Prop erty

A new common fixed point result for a countable family of non-self mappings defined on a closed subset of a cone metric space with the convex property is obtained, and from which, a more general result is given. Our main results improve and generalize many known common fixed point theorems.     

APPROXIMATION OF FIXED POINTS AND VARIATIONAL SOLUTIONS FOR PSEUDO-CONTRACTIVE MAPPINGS IN BANACH SPACES

Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gteaux differentiable norm. Assume that every nonempty closed convex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive mappings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, convex optimization problems, and split feasibility problems. Our result extends many recent important results.     

COMMON FIXED POINT THEOREMS FOR MULTI-VALUED MAPS

We establish some results on coincidence and common fixed points for a twopair of multi-valued and single-valued maps in complete metric spaces.Presented theorems generalize recent results of Gordji et...     

Strong convergence theorems of common elements for equilibrium problems and fixed point problems in banach spaces

In this paper,we consider hybrid algorithms for finding common elements of the set of common fixed points of two families quasi-φ-non-expansive mappings and the set of solutions of an equilibrium problem.We establish strong convergence theorems of common elements in uniformly smooth and strictly convex Banach spaces with the property (K).     

锥距离空间中压缩条件下的公共不动点定理(英文)

In order to develop and improve the fixed point theorems in cone metric spaces, some new fixed point theorems are presented for two mappings in cone metric spaces which satisfy contractive conditions, where the cone is not necessarily normal. Our results generalize fixed point theorems of Abbas, Jungck and Stojan Radenovi in cone metric spaces.     

FIXED POINT RESULTS ON METRIC-TYPE SPACES

In this paper we obtain fixed point and common fixed point theorems for self- mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results.     

非线性混合似变分不等式的扰动近似点-投影算法

In this paper we introduce a new perturbed proximal-projection algorithm for finding the common element of the set of fixed points of non-expansive mappings and the set of solutions of nonlinear mixed variational-like inequalities. The convergence criteria of the iterative sequences generated by the new iterative algorithm is also given. Our approach and results generalize many known results in this field.     

Fixed Points of Nonexpansive Type Mappings in Topological Spaces

Recently. Penot[1] and Kirk[2]obtained the abstract versions of Kirk's fixed point theorem of [3] for nonexpansive mappings, respectively. Gille spie and Williams [4, 5] replaced the reflexive and normal structure used in Kirk [3] and Kannan [6], by uniformly normal structure to obtain the fixed point theorems for nonexpansive and Kannan mappings. Kaukich [7] also extended the result of [3] to the generalized nonexpansive mappings.     

GENERALIZED NONEXPANSIVE TYPE MAPPINGS AND COMMON FIXED POINT THEOREMS IN BANACH SPACES

We obtained some fixed point theorems for average nonexpansive mappings.[1,2]The main purpose of the present paper is to extend our results to cases of generalized nonexpansive type mappings and common fixed point.     

COMMON FIXED POINT THEOREMS FOR THREE MAPS IN DISCONTINUOUS Gb-METRIC SPACES

In [Aghajani A, Abbas M, Roshan JR. Common fixed point of generalized weak contractive mappings in partially ordered Gb-metric spaces. Filomat, 2013, in press], using the concepts of G-metric and b-metric Aghajani et al. defined a new type of metric which is called generalized b-metric or Gb-metric. In this paper, we prove a common fixed point theorem for three mappings in Gb-metric space which is not continuous. An example is presented to verify the effectiveness and applicability of our main result.