• Title/Summary/Keyword: $\mathcal{H}$ Simulation functions

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𝓗-SIMULATION FUNCTIONS AND Ωb-DISTANCE MAPPINGS IN THE SETTING OF Gb-METRIC SPACES AND APPLICATION

  • Tariq Qawasmeh
    • Nonlinear Functional Analysis and Applications
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    • v.28 no.2
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    • pp.557-570
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    • 2023
  • The conceptions of generalized b-metric spaces or Gb-metric spaces and a generalized Ω-distance mappings play a key role in proving many important theorems in existence and uniqueness of fixed point theory. In this manuscript, we establish a new type of contraction namely, Ωb(𝓗, 𝜃, s)-contraction, this contraction based on the concept of a generalized Ω-distance mappings which established by Abodayeh et.al. in 2017 together with the concept of 𝓗-simulation functions which established by Bataihah et.al [10] in 2020. By utilizing this new notion we prove new results in existence and uniqueness of fixed point. On the other hand, examples and application were established to show the importance of our results.

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.