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Fixed point theorems for hybrid mappings.

Maria Samreen1, Tayyab Kamran2, Erdal Karapinar3

  • 1School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad 44000, Pakistan.

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Summary
This summary is machine-generated.

This study establishes new fixed point theorems for hybrid mappings, generalizing existing results and introducing a novel concept of generalized occasionally weak compatibility. The findings are supported by illustrative examples.

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Area of Science:

  • Mathematics
  • Fixed Point Theory
  • Nonlinear Analysis

Background:

  • Fixed point theory is crucial for solving equations in various scientific fields.
  • Hybrid mappings and tangential properties are advanced concepts in metric spaces.
  • Existing theorems by Babu and Alemayehu provide a foundation for this research.

Purpose of the Study:

  • To establish novel fixed point theorems for two pairs of hybrid mappings.
  • To generalize existing fixed point results using specific contractive conditions.
  • To introduce and explore a new concept generalizing occasionally weak compatibility.

Main Methods:

  • Application of hybrid tangential property.
  • Utilizing quadratic type contractive conditions.
  • Development of a new notion for generalized occasionally weak compatibility.

Main Results:

  • Derivation of new fixed point theorems for hybrid mappings.
  • Demonstration of generalization of prior results by Babu and Alemayehu.
  • Introduction of a novel concept of generalized occasionally weak compatibility.

Conclusions:

  • The established theorems offer broader applicability in fixed point theory.
  • The new concept enhances the understanding of mapping properties.
  • Concrete examples validate the significance and generality of the results.