UNIQUE COMMON FIXED POINT OF A FAMILY OF SELF-MAPS WITH SAME TYPE CONTRACTIVE CONDITION IN 2-METRIC SPACE

In this paper, we prove that a family of self-maps {Ti,j}i,j∈N in 2-metric space has a unique common fixed point if （i） {Ti,j}i,j∈N satisfies the same type contractive condition for each j ∈ N; （ii） Tm,μ .Tn,v = Tn,v.Tm.μ for all m,n,μ,v ∈ N with μ≠v. Our main result generalizes and improves many known unique common fixed point theorems in 2-metric spaces.

New Unique Common Fixed Point Results for Four Mappings with Ф-Contractive Type in 2-Metric Spaces

In this paper, some new unique common fixed points for four mappings satisfying Ф-contractive conditions on non-complete 2-metric spaces are obtained, in which the mappings do not satisfy continuity and commutation. The main results generalize and improve many well-known and corresponding conclusions in the literatures.

Four Mappings Satisfying Ψ-Contractive Type Condition and Having Unique Common Fixed Point on 2-Metric Spaces

In this paper, we introduce a class Ψ of real functions defined on the set of non-negative real numbers, and obtain a new unique common fixed point theorem for four mappings satisfying Ψ-contractive condition on a non-complete 2-metric space and give the versions of the corresponding result for two and three mappings.

New Fixed Point Results of Generalized g-Quasi-Contractions in Cone b-Metric Spaces Over Banach Algebras

In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.

An Improvement of a Known Unique Common Fixed Point Result for Four Mappings on 2-Metric Spaces

In this paper, we introduce a new class Γ, which is weak than a known class Ψ, of real continuous functions defined on [0, +∞), and use another method to prove the known unique common fixed point theorem for four mappings with γ-contractive condition instead of Ψ-contractive condition on 2-metric spaces.

A Family of Non-Self Maps Satisfying <i>Φ</i>_i-Contractive Condition and Having Unique Common Fixed Point in Metrically Convex Spaces

Class of 5-dimensional functions Φ was introduced and a convergent sequence determined by non-self mappings satisfying certain Φi-contractive condition was constructed, and then that the limit of the sequence is the unique com-mon fixed point of the mappings was proved. Finally, several more general forms were given. Our main results gener-alize and unify many same type fixed point theorems in references.

Points of Coincidence and Common Fixed Points for Ⅱ-Expansive Mappings on Complex Valued Metric Spaces

Abstract. We use the two mappings satisfying II-expansive conditions on complex valued metric spaces to construct the convergent sequences and prove that the unique limit of the sequences is the point of coincidence or common fixed point of the two mappings. Also, we discuss the uniqueness of points of coincidence or common fixed points and give the existence theorems of unique fixed points. The obtained results generalize and improve the corresponding conclusions in references.

ON COLLECTIVELY FIXED POINT THEOREMS ON FC-SPACES

Based on a KKM type theorem on FC-space, some new fixed point theorems for Fan-Browder type are established, and then some collectively fixed point theorems for a family of Ф-maps defined on product space of FC-spaces are given.These results generalize and improve many corresponding results.

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

A class Ф of 5-dimensional functions was introduced and an existence and uniqueness of common fixed points for a family of non-self mappings satisfying a Фi- quasi-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.

Common Fixed Points for Two Contractive Mappings of Integral Type in Metric Spaces

In this paper, we obtain unique common fixed point theorems for two mappings satisfying the variable coefficient linear contraction of integral type and the implicit contraction of integral type respectively in metric spaces.

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.

Common Fixed Points for a Countable Family of Set-Valued Mappings with Quasi-Contractive Conditions on Metrically Convex Spaces

In this paper, we consider a countable family of set-valued mappings satisfying some quasi-contractive conditions. We also construct a sequence by the quasi-contractive conditions of mappings and the boundary condition of a closed subset of a metrically convex space, and then prove that the unique limit of the sequence is the unique common fixed point of the mappings. Finally, we give more generalized common fixed point theorems for a countable family of single-valued mappings. The main results generalize and improve many common fixed point theorems for a finite or countable family of single valued or set-valued mappings with quasi-contractive conditions.

Fixed Points and Common Fixed Points of Quasi-Contractive Mappings on Partially Ordered-Cone Metric Spaces

In this paper, we use the mappings with quasi-contractive conditions, defined on a partially ordered set with cone metric structure, to construct convergent sequences and prove that the limits of the constructed sequences are the unique (common) fixed point of the mappings, and give their corollaries. The obtained results improve and generalize the corresponding conclusions in references.