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Fixed points of contractive mappings in b-metric-like spaces.

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A hybrid common fixed point theorem under certain recent properties.

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This study proves a common fixed point theorem for hybrid pairs of occasionally coincidentally idempotent mappings using the common limit range property. The findings enhance existing literature, particularly work by Sintunavarat and Kumam (2009).

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Area of Science:

  • Fixed-point theory
  • Nonlinear analysis
  • Metric spaces

Background:

  • Fixed-point theorems are fundamental in nonlinear analysis.
  • Occasionally coincidentally idempotent mappings and common limit range properties are advanced concepts.
  • Existing theorems may have limitations in broader applications.

Purpose of the Study:

  • To establish a new common fixed point theorem.
  • To generalize and improve upon existing results in fixed-point theory.
  • To introduce the common limit range property for hybrid pairs.

Main Methods:

  • Utilizing the common limit range property.
  • Developing a hybrid pair of occasionally coincidentally idempotent mappings.
  • Proving a common fixed point theorem.

Main Results:

  • A novel common fixed point theorem is proven.
  • The theorem generalizes and improves upon prior results, notably Sintunavarat and Kumam (2009).
  • Illustrative examples demonstrate the theorem's efficacy and improvements.

Conclusions:

  • The established common fixed point theorem offers a significant advancement.
  • The common limit range property provides a powerful tool for fixed-point theory.
  • The findings contribute to the broader understanding of mappings in metric spaces.