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...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.展开更多
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. ...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.展开更多
In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contracti...In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contractive condition, where ΦjεΦ, for each jεN;2) Tm,μ n,v for all m,n,μ,vεN with μ ≠ v . Our main result generalizes and unifies many known unique common fixed point theorems in 2-metric spaces.展开更多
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 n...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.展开更多
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 m...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.展开更多
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 ...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.展开更多
Projective change between two Finsler metrics arises from Information Geom-etry. Such metrics have special geometric properties and will play an important role in Finsler geometry. The purpose of the present paper is ...Projective change between two Finsler metrics arises from Information Geom-etry. Such metrics have special geometric properties and will play an important role in Finsler geometry. The purpose of the present paper is to find a relation to characterize the projective change between generalized (α, β) - metric ( μ1, μ2 and μ3 ≠ 0 are constants) and Randers metric , where α and are two Riemannian metrics, β and are 1-forms. Further, we study such projective change when generalized (α, β) -metric F has some curvature property.展开更多
In this paper, minimal submanifolds in Finsler spaces with (α, β)-metrics are studied. Especially, helicoids are also minimal in (α, β)-Minkowski spaces. Then the minimal surfaces of conoid in Finsler spaces with ...In this paper, minimal submanifolds in Finsler spaces with (α, β)-metrics are studied. Especially, helicoids are also minimal in (α, β)-Minkowski spaces. Then the minimal surfaces of conoid in Finsler spaces with (α, β)-metrics are given. Last, the Gauss curvature of the conoid in the 3-dimension Randers-Minkowski space is studied.展开更多
In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function ? to construct a new implicit-linear contractive condition and obtain some existence theorems of commo...In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function ? to construct a new implicit-linear contractive condition and obtain some existence theorems of common fixed points for two mappings on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point. The obtained results goodly generalize and improve the corresponding conclusions in references.展开更多
In this paper,we introduce the notion of generalized cyclic contraction pairs in b2-metric spaces and establish some fixed point theorems for such pairs.Then,we give an example to illustrate our results.
In this paper,we study the(α,β)-metrics of constant flag curvature.We characterize almost regular(α,β)-metrics of constant flag curvature under the condition that β is a homothetic 1-form with respect to a.Furthe...In this paper,we study the(α,β)-metrics of constant flag curvature.We characterize almost regular(α,β)-metrics of constant flag curvature under the condition that β is a homothetic 1-form with respect to a.Furthermore,we prove that if a regular(α,β)-metric is of constant flag curvature and β is a Killing 1-form with constant length,then it must be a Riemannian metric or locally Minkowskian.展开更多
In this paper,we study the projectively Ricci-flat general(α,β)-metrics within to a spray framework and also bring out the rich variety of behaviour displayed by an important projective invariant.Projective Ricci cu...In this paper,we study the projectively Ricci-flat general(α,β)-metrics within to a spray framework and also bring out the rich variety of behaviour displayed by an important projective invariant.Projective Ricci curvature is one of the essential projective invariant in Finsler geometry which has been introduced by Z.Shen.The projective Ricci curvature is defined as Ricci curvature of a projective spray associated with a given spray G on M^(n) with a volume form dV on M^(n).展开更多
Abstract In this article, the author studies the projectively flat Matsumoto metric F=α^2/（α -β）, where α=√αijy^iy^j is a Riemannian metric and β =biy^i is 1-form. Theyconclude that α is locally projectively...Abstract In this article, the author studies the projectively flat Matsumoto metric F=α^2/（α -β）, where α=√αijy^iy^j is a Riemannian metric and β =biy^i is 1-form. Theyconclude that α is locally projectively fiat and β is paralled with respect to α. And get the same result for the higher order approximate Matsumoto metric.展开更多
文摘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.
文摘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.
文摘In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contractive condition, where ΦjεΦ, for each jεN;2) Tm,μ n,v for all m,n,μ,vεN with μ ≠ v . Our main result generalizes and unifies many known unique common fixed point theorems in 2-metric spaces.
文摘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.
文摘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.
文摘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.
文摘Projective change between two Finsler metrics arises from Information Geom-etry. Such metrics have special geometric properties and will play an important role in Finsler geometry. The purpose of the present paper is to find a relation to characterize the projective change between generalized (α, β) - metric ( μ1, μ2 and μ3 ≠ 0 are constants) and Randers metric , where α and are two Riemannian metrics, β and are 1-forms. Further, we study such projective change when generalized (α, β) -metric F has some curvature property.
文摘In this paper, minimal submanifolds in Finsler spaces with (α, β)-metrics are studied. Especially, helicoids are also minimal in (α, β)-Minkowski spaces. Then the minimal surfaces of conoid in Finsler spaces with (α, β)-metrics are given. Last, the Gauss curvature of the conoid in the 3-dimension Randers-Minkowski space is studied.
文摘In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function ? to construct a new implicit-linear contractive condition and obtain some existence theorems of common fixed points for two mappings on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point. The obtained results goodly generalize and improve the corresponding conclusions in references.
文摘In this paper,we introduce the notion of generalized cyclic contraction pairs in b2-metric spaces and establish some fixed point theorems for such pairs.Then,we give an example to illustrate our results.
基金supported by the NationalNatural Science Foundation of China(11871126)the Science Foundation of Chongqing Normal University(17XLB022)。
文摘In this paper,we study the(α,β)-metrics of constant flag curvature.We characterize almost regular(α,β)-metrics of constant flag curvature under the condition that β is a homothetic 1-form with respect to a.Furthermore,we prove that if a regular(α,β)-metric is of constant flag curvature and β is a Killing 1-form with constant length,then it must be a Riemannian metric or locally Minkowskian.
文摘In this paper,we study the projectively Ricci-flat general(α,β)-metrics within to a spray framework and also bring out the rich variety of behaviour displayed by an important projective invariant.Projective Ricci curvature is one of the essential projective invariant in Finsler geometry which has been introduced by Z.Shen.The projective Ricci curvature is defined as Ricci curvature of a projective spray associated with a given spray G on M^(n) with a volume form dV on M^(n).
文摘Abstract In this article, the author studies the projectively flat Matsumoto metric F=α^2/（α -β）, where α=√αijy^iy^j is a Riemannian metric and β =biy^i is 1-form. Theyconclude that α is locally projectively fiat and β is paralled with respect to α. And get the same result for the higher order approximate Matsumoto metric.
