• Title/Summary/Keyword: Generalized metric spaces

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GENERALIZED VECTOR MINTY'S LEMMA

  • Lee, Byung-Soo
    • The Pure and Applied Mathematics
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    • v.19 no.3
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    • pp.281-288
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    • 2012
  • In this paper, the author defines a new generalized ${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mapping and considers the equivalence of Stampacchia-type vector variational-like inequality problems and Minty-type vector variational-like inequality problems for generalized (${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mappings in Banach spaces, called the generalized vector Minty's lemma.

COUPLED COINCIDENCE POINT RESULTS FOR GENERALIZED SYMMETRIC MEIR-KEELER CONTRACTION ON PARTIALLY ORDERED METRIC SPACES WITH APPLICATION

  • Deshpande, Bhavana;Handa, Amrish
    • The Pure and Applied Mathematics
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    • v.24 no.2
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    • pp.79-98
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    • 2017
  • We establish a coupled coincidence point theorem for generalized compatible pair of mappings $F,G:X{\times}X{\rightarrow}X$ under generalized symmetric Meir-Keeler contraction on a partially ordered metric space. We also deduce certain coupled fixed point results without mixed monotone property of $F:X{\times}X{\rightarrow}X$. An example supporting to our result has also been cited. As an application the solution of integral equations are obtain here to illustrate the usability of the obtained results. We improve, extend and generalize several known results.

EXISTENCE OF COINCIDENCE POINT UNDER GENERALIZED NONLINEAR CONTRACTION WITH APPLICATIONS

  • Deshpande, Bhavana;Handa, Amrish;Thoker, Shamim Ahmad
    • East Asian mathematical journal
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    • v.32 no.3
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    • pp.333-354
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    • 2016
  • We present coincidence point theorem for g-non-decreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings $F,G:X^2{\rightarrow}X$ by using obtained coincidence point results. Furthermore, an example and an application to integral equation are also given to show the usability of obtained results. Our results generalize, modify, improve and sharpen several well-known results.

GENERALIZED m-QUASI-EINSTEIN STRUCTURE IN ALMOST KENMOTSU MANIFOLDS

  • Mohan Khatri;Jay Prakash Singh
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.3
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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.

NONLINEAR MAPPINGS IN METRIC AND HAUSDORFF SPACES AND THEIR COMMON FIXED POINT

  • Som, Tanmoy
    • Kyungpook Mathematical Journal
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    • v.28 no.1
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    • pp.97-106
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    • 1988
  • In the first section of this paper two common fixed point results for four nonlinear mappings which are pairwise commuting and only two of them being continuous have been given on a complete metric space and on a compact metric space respectively which generalize the results of Mukherjee [2] and Yeh [4]. Further two common fixed point theorems have been established for two finite families of non linear mappings, with only one family being continuous. In another section we extend Theorem 3 and Theorem 4 of Mukherjee [2] for common fixed point of four continuous mappings on a Hausdorff space and on a compact metric space respectively. In the same spaces, these two results have been further generalized for two finite families of continuous mappings.

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COMMON FIXED POINT AND INVARIANT APPROXIMATION IN MENGER CONVEX METRIC SPACES

  • Hussain, Nawab;Abbas, Mujahid;Kim, Jong-Kyu
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.4
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    • pp.671-680
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    • 2008
  • Necessary conditions for the existence of common fixed points for noncommuting mappings satisfying generalized contractive conditions in a Menger convex metric space are obtained. As an application, related results on best approximation are derived. Our results generalize various well known results.

COMMON FIXED POINTS AND INVARIANT APPROXIMATIONS FOR SUBCOMPATIBLE MAPPINGS IN CONVEX METRIC SPACE

  • Nashine, Hemant Kumar;Kim, Jong-Kyu
    • East Asian mathematical journal
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    • v.26 no.1
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    • pp.39-47
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    • 2010
  • Existence of common fixed points for generalized S-nonexpansive subcompatible mappings in convex metric spaces have been obtained. Invariant approximation results have also been derived by its application. These results extend and generalize various known results in the literature with the aid of more general class of noncommuting mappings.

COUPLED FIXED POINT THEOREMS OF SOME CONTRACTION MAPS OF INTEGRAL TYPE ON CONE METRIC SPACES OVER BANACH ALGEBRAS

  • Akewe, Hudson;Olilima, Joshua;Mogbademu, Adesanmi
    • Honam Mathematical Journal
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    • v.43 no.2
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    • pp.269-287
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    • 2021
  • In this paper, we prove some coupled fixed point theorems satisfying some generalized contractive condition in a cone metric space over a Banach algebra. We also applied the results obtained to show coupled fixed point of some contractive mapping of integral type.

The extension of the largest generalized-eigenvalue based distance metric Dij1) in arbitrary feature spaces to classify composite data points

  • Daoud, Mosaab
    • Genomics & Informatics
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    • v.17 no.4
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    • pp.39.1-39.20
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    • 2019
  • Analyzing patterns in data points embedded in linear and non-linear feature spaces is considered as one of the common research problems among different research areas, for example: data mining, machine learning, pattern recognition, and multivariate analysis. In this paper, data points are heterogeneous sets of biosequences (composite data points). A composite data point is a set of ordinary data points (e.g., set of feature vectors). We theoretically extend the derivation of the largest generalized eigenvalue-based distance metric Dij1) in any linear and non-linear feature spaces. We prove that Dij1) is a metric under any linear and non-linear feature transformation function. We show the sufficiency and efficiency of using the decision rule $\bar{{\delta}}_{{\Xi}i}$(i.e., mean of Dij1)) in classification of heterogeneous sets of biosequences compared with the decision rules min𝚵iand median𝚵i. We analyze the impact of linear and non-linear transformation functions on classifying/clustering collections of heterogeneous sets of biosequences. The impact of the length of a sequence in a heterogeneous sequence-set generated by simulation on the classification and clustering results in linear and non-linear feature spaces is empirically shown in this paper. We propose a new concept: the limiting dispersion map of the existing clusters in heterogeneous sets of biosequences embedded in linear and nonlinear feature spaces, which is based on the limiting distribution of nucleotide compositions estimated from real data sets. Finally, the empirical conclusions and the scientific evidences are deduced from the experiments to support the theoretical side stated in this paper.