• Title/Summary/Keyword: $\Omega$-distance mapping

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A NEW CONTRACTION BY UTILIZING H-SIMULATION FUNCTIONS AND Ω-DISTANCE MAPPINGS IN THE FRAME OF COMPLETE G-METRIC SPACES

  • AHMED AL-ZGHOUL;TARIQ QAWASMEH;RAED HATAMLEH;ABEDALKAREEM ALHAZIMEH
    • Journal of applied mathematics & informatics
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    • v.42 no.4
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    • pp.749-759
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    • 2024
  • In this manuscript, we formulate the notion of Ω(H, θ)-contraction on a self mapping f : W → W, this contraction based on the concept of Ω-distance mappings equipped on G-metric spaces together with the concept of H-simulation functions and the class of Θ-functions, we employ our new contraction to unify the existence and uniqueness of some new fixed point results. Moreover, we formulate a numerical example and a significant application to show the novelty of our results; our application is based on the significant idea that the solution of an equation in a certain condition is similar to the solution of a fixed point equation. We are utilizing this idea to prove that the equation, under certain conditions, not only has a solution as the Intermediate Value Theorem says but also that this solution is unique.

𝓗(ω, θ)-CONTRACTION AND SOME NEW FIXED POINT RESULTS IN MODIFIED ω-DISTANCE MAPPINGS VIA COMPLETE QUASI METRIC SPACES AND APPLICATION

  • Abedalkareem Alhazimeh;Raed Hatamleh
    • Nonlinear Functional Analysis and Applications
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    • v.28 no.2
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    • pp.395-405
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    • 2023
  • In this manuscript, we establish the concept of 𝓗(ω, θ)-contraction which based on modified ω distance mappings which introduced by Alegre and Marin [4] in 2016 and 𝓗 simulation functions which introduced by Bataihah et.al. [14] in 2020 and we employ our contraction to prove the existence and uniqueness some new fixed point results. On the other hand, we create some examples and an application to show the importance of our results.