• Title/Summary/Keyword: G-metric space

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EINSTEIN LIGHTLIKE HYPERSURFACES OF A LORENTZIAN SPACE FORM WITH A SEMI-SYMMETRIC METRIC CONNECTION

  • Jin, Dae Ho
    • Communications of the Korean Mathematical Society
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    • v.28 no.1
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    • pp.163-175
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    • 2013
  • In this paper, we prove a classification theorem for Einstein lightlike hypersurfaces M of a Lorentzian space form ($\bar{M}$(c), $\bar{g}$) with a semi-symmetric metric connection subject such that the second fundamental forms of M and its screen distribution S(TM) are conformally related by some non-zero constant.

COINCIDENCE AND FIXED POINT RESULTS FOR GENERALIZED WEAK CONTRACTION MAPPING ON b-METRIC SPACES

  • Malkawi, Abed Al-Rahman M.;Talafhah, Abdallah;Shatanawi, Wasfi
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.1
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    • pp.177-195
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    • 2021
  • In this paper, we introduce the modification of a generalized (Ψ, L)-weak contraction and we prove some coincidence point results for self-mappings G, T and S, and some fixed point results for some maps by using a (c)-comparison function and a comparison function in the sense of a b-metric space.

FIXED POINT THEOREMS FOR (𝜉, 𝛽)-EXPANSIVE MAPPING IN 𝒢-METRIC SPACE USING CONTROL FUNCTION

  • Yadav, Jyoti;Kumar, Manoj;Reena, Reena;Imdad, Mohammad;Arora, Sahil
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.5
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    • pp.949-959
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    • 2021
  • In this paper, some fixed point theorems for new type of (𝜉, 𝛽)-expansive mappings of type (S) and type (T) using control function and 𝛽-admissible function in 𝒢-metric spaces are proved. Further, we prove certain fixed point results by relaxing the continuity condition.

REMARKS ON CERTAIN NOTED COINCIDENCE THEOREMS: A UNIFYING AND ENRICHING APPROACH

  • Alam, Aftab;Hasan, Mohd.;Imdad, Mohammad
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.5
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    • pp.1059-1075
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    • 2021
  • In this paper, we unify and enrich the well-known classical metrical coincidence theorems on a complete metric space due to Machuca, Goebel and Jungck. We further extend our newly proved results on a subspace Y of metric space X, wherein X need not be complete. Finally, we slightly modify the existing results involving (E.A)-property and (CLRg)-property and apply these results to deduce our coincidence and common fixed point theorems.

COMMON FIXED POINT THEOREMS OF MEIR-KEELER TYPE ON MULTIPLICATIVE METRIC SPACES

  • DESHPANDE, BHAVANA;SHEIKH, SAJAD AHMAD
    • The Pure and Applied Mathematics
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    • v.23 no.2
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    • pp.131-143
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    • 2016
  • In this paper, we present some common fixed point theorems for two pairs of weakly compatible self-mappings on multiplicative metric spaces satisfying a generalized Meir-Keeler type contractive condition. The results obtained in this paper extend, improve and generalize some well known comparable results in literature.

ALMOST EINSTEIN MANIFOLDS WITH CIRCULANT STRUCTURES

  • Dokuzova, Iva
    • Journal of the Korean Mathematical Society
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    • v.54 no.5
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    • pp.1441-1456
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    • 2017
  • We consider a 3-dimensional Riemannian manifold M with a circulant metric g and a circulant structure q satisfying $q^3=id$. The structure q is compatible with g such that an isometry is induced in any tangent space of M. We introduce three classes of such manifolds. Two of them are determined by special properties of the curvature tensor. The third class is composed by manifolds whose structure q is parallel with respect to the Levi-Civita connection of g. We obtain some curvature properties of these manifolds (M, g, q) and give some explicit examples of such manifolds.

Conformally flat cosymplectic manifolds

  • Kim, Byung-Hak;Kim, In-Bae
    • Communications of the Korean Mathematical Society
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    • v.12 no.4
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    • pp.999-1006
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    • 1997
  • We proved that if a fibred Riemannian space $\tilde{M}$ with cosymplectic structure is conformally flat, then $\tilde{M}$ is the locally product manifold of locally Euclidean spaces, that is locally Euclidean. Moreover, we investigated the fibred Riemannian space with cosymplectic structure when the Riemannian metric $\tilde{g}$ on $\tilde{M}$ is Einstein.

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INNOVATION FIXED POINT THEOREMS IN 0-σ-COMPLETE METRIC-LIKE SPACES WITH APPLICATION IN INTEGRAL EQUATIONS

  • Ranjbar, Ghorban Khalilzadeh
    • The Pure and Applied Mathematics
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    • v.29 no.3
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    • pp.231-244
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    • 2022
  • In this paper, we introduce the notion of rational g-h-ϕ-weak contractions in tripled metric-like spaces and demonstrate common fixed point results for each mappings in 0-σ complete tripled metric-like spaces and some examples and application are given.