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The current topic is about an extended probabilistic \(C-\) contraction. Probable extension of metric spaces is known as Probabilistic metric spaces. We develop a fixed-point result of substituting the constant term by functional. This kind of contraction generalizes several previous fixed-point findings. Finally, we are able to present a unique fixed point solution for such a contraction. An illustrative example of a heat equation with a local internal controller is also provided to verify our primary conclusion.

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Probabilistic Contraction Result Involving Functionals in Menger Space and Heat Equation

  • 章节

  • 发表日期：

    2026年

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  • Samir Kumar Bhandari,
  • Pulak Konar,
  • Rabha W. Ibrahim,
  • Anita Tomar

摘要

The current topic is about an extended probabilistic \(C-\) contraction. Probable extension of metric spaces is known as Probabilistic metric spaces. We develop a fixed-point result of substituting the constant term by functional. This kind of contraction generalizes several previous fixed-point findings. Finally, we are able to present a unique fixed point solution for such a contraction. An illustrative example of a heat equation with a local internal controller is also provided to verify our primary conclusion.