• 제목/요약/키워드: G-metric space

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COUPLED COINCIDENCE POINT RESULTS WITH MAPPINGS SATISFYING RATIONAL INEQUALITY IN PARTIALLY ORDERED METRIC SPACES

  • CHOUDHURY, BINAYAK S.;KONAR, PULAK;METIYA, NIKHILESH
    • Journal of applied mathematics & informatics
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    • 제37권1_2호
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    • pp.1-11
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    • 2019
  • In this paper we prove certain coupled coincidence point and coupled common fixed point results in partially ordered metric spaces for a pair of compatible mappings which satisfy certain rational inequality. The results are supported with two examples.

COINCIDENCE POINT AND FIXED POINT THEOREMS IN PARTIAL METRIC SPACES FOR CONTRACTIVE TYPE MAPPINGS WITH APPLICATIONS

  • SALUJA, G.S.;KIM, JONG KYU;LIM, WON HEE
    • Journal of applied mathematics & informatics
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    • 제40권5_6호
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    • pp.1053-1071
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    • 2022
  • The purpose of this article is to establish some fixed point theorems, a common fixed point theorem and a coincidence point theorem via contractive type condition in the framework of complete partial metric spaces and give some examples in support of our results. As an application to the results, we give some fixed point theorems for integral type contractive conditions. The results presented in this paper extend and generalize several results from the existing literature.

GENERALIZED INTEGRAL TYPE F-CONTRACTION IN PARTIAL METRIC SPACES AND COMMON FIXED POINT

  • G. S. Saluja;Ho Geun Hyun;Jong Kyu Kim
    • Nonlinear Functional Analysis and Applications
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    • 제28권1호
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    • pp.107-121
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    • 2023
  • In this work, we study generalized integral type F-contractions in partial metric spaces and establish some common fixed point theorems. Also, we give some consequences of the established result. Our results extend and generalize several results from the existing literature.

ON COUPLED COINCIDENCE POINTS IN MULTIPLICATIVE METRIC SPACES WITH AN APPLICATION

  • Ibtisam Mutlaq Alanazi;Qamrul Haque Khan;Shahbaz Ali;Tawseef Rashid;Faizan Ahmad Khan
    • Nonlinear Functional Analysis and Applications
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    • 제28권3호
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    • pp.775-791
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    • 2023
  • In this manuscript, we prove the existence of the coupled coincidence point by using g-couplings in multiplicative metric spaces (MMS). Further we show that existence of a fixed point in ordered MMS having t-property. Finally, some examples and application are presented for attesting to the credibility of our results.

FIXED POINT THEOREMS FOR A PAIR OF (α, η, ψ)-GERAGHTY CONTRACTION TYPE MAPS IN COMPLETE METRIC SPACES

  • P. Sudheer Kumar;G. V. V. Jagannadha Rao;R. Santhi Kumar;P. E. Satyanarayana
    • Nonlinear Functional Analysis and Applications
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    • 제29권1호
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    • pp.57-67
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    • 2024
  • In this paper, we prove the existence of common fixed point for a pair of α-η-ψ-Geraghty contraction type maps in complete metric spaces using new type of α-admissible. These results extend and generalize some of the previously known results.

SOME GENERAL CONVERGENCE PRINCIPLES WITH APPLICATIONS

  • Zhou, H.Y.;Gao, G.L.;Guo, G.T.;Cho, Y.J.
    • 대한수학회보
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    • 제40권3호
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    • pp.351-363
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    • 2003
  • In the present paper, some general convergence principles are established in metric spaces and then theses principles are applied to the convergence of the iterative sequences for approximating fixed points of certain classes of mappings. By virtue of our principles, most of the latest results obtained by several authors can be deduced easily.

COMMON FIXED POINT THEOREMS FOR GENERALIZED 𝜓∫𝜑-WEAKLY CONTRACTIVE MAPPINGS IN G-METRIC SPACES

  • Kim, Jong Kyu;Kumar, Manoj;Bhardwaj, Preeti;Imdad, Mohammad
    • Nonlinear Functional Analysis and Applications
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    • 제26권3호
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    • pp.565-580
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    • 2021
  • In this paper, first of all we prove a fixed point theorem for 𝜓∫𝜑-weakly contractive mapping. Next, we prove some common fixed point theorems for a pair of weakly compatible self maps along with E.A. property and (CLR) property. An example is also given to support our results.

DEFORMATION SPACES OF CONVEX REAL-PROJECTIVE STRUCTURES AND HYPERBOLIC AFFINE STRUCTURES

  • Darvishzadeh, Mehdi-Reza;William M.Goldman
    • 대한수학회지
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    • 제33권3호
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    • pp.625-639
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    • 1996
  • A convex $RP^n$-structure on a smooth anifold M is a representation of M as a quotient of a convex domain $\Omega \subset RP^n$ by a discrete group $\Gamma$ of collineations of $RP^n$ acting properly on $\Omega$. When M is a closed surface of genus g > 1, then the equivalence classes of such structures form a moduli space $B(M)$ homeomorphic to an open cell of dimension 16(g-1) (Goldman [2]). This cell contains the Teichmuller space $T(M)$ of M and it is of interest to know what of the rich geometric structure extends to $B(M)$. In [3], a symplectic structure on $B(M)$ is defined, which extends the symplectic structure on $T(M)$ defined by the Weil-Petersson Kahler form.

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GENERALIZED m-QUASI-EINSTEIN STRUCTURE IN ALMOST KENMOTSU MANIFOLDS

  • Mohan Khatri;Jay Prakash Singh
    • 대한수학회보
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    • 제60권3호
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    • pp.717-732
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    • 2023
  • The goal of this paper is to analyze the generalized m-quasi-Einstein structure in the context of almost Kenmotsu manifolds. Firstly we showed that a complete Kenmotsu manifold admitting a generalized m-quasi-Einstein structure (g, f, m, λ) is locally isometric to a hyperbolic space ℍ2n+1(-1) or a warped product ${\tilde{M}}{\times}{_{\gamma}{\mathbb{R}}$ under certain conditions. Next, we proved that a (κ, µ)'-almost Kenmotsu manifold with h' ≠ 0 admitting a closed generalized m-quasi-Einstein metric is locally isometric to some warped product spaces. Finally, a generalized m-quasi-Einstein metric (g, f, m, λ) in almost Kenmotsu 3-H-manifold is considered and proved that either it is locally isometric to the hyperbolic space ℍ3(-1) or the Riemannian product ℍ2(-4) × ℝ.

RIEMANNIAN SUBMERSIONS OF SO0(2, 1)

  • Byun, Taechang
    • 대한수학회지
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    • 제58권6호
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    • pp.1407-1419
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    • 2021
  • The Iwasawa decomposition NAK of the Lie group G = SO0(2, 1) with a left invariant metric produces Riemannian submersions G → N\G, G → A\G, G → K\G, and G → NA\G. For each of these, we calculate the curvature of the base space and the lifting of a simple closed curve to the total space G. Especially in the first case, the base space has a constant curvature 0; the holonomy displacement along a (null-homotopic) simple closed curve in the base space is determined only by the Euclidean area of the region surrounded by the curve.