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Some endpoint results for β-generalized weak contractive multifunctions.

H Alikhani1, D Gopal2, M A Miandaragh1

  • 1Department of Mathematics, Azarbaijan University of Shahid Madani, Azarshahr, Tabriz, Iran.

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Summary
This summary is machine-generated.

This study introduces a new type of mathematical function called β-generalized weak contractive multifunctions. Researchers explored their endpoint properties and the influence of specific points on endpoint existence.

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Area of Science:

  • Mathematical Analysis
  • Fixed-Point Theory
  • Set-Valued Analysis

Background:

  • Multifunctions are fundamental in various mathematical fields.
  • Understanding endpoint properties is crucial for analyzing function behavior.
  • Existing contractive conditions have limitations in broader applications.

Purpose of the Study:

  • To introduce and define β-generalized weak contractive multifunctions.
  • To investigate the existence and properties of endpoints for these multifunctions.
  • To analyze the role of specific points in guaranteeing endpoint existence.

Main Methods:

  • Development of a new class of multifunctions (β-generalized weak contractive).
  • Application of fixed-point theorems and related analytical techniques.
  • Exploration of endpoint characterizations and existence criteria.

Main Results:

  • Established theoretical results concerning β-generalized weak contractive multifunctions.
  • Provided conditions for the existence of endpoints.
  • Demonstrated the significance of certain points in endpoint determination.

Conclusions:

  • The introduction of β-generalized weak contractive multifunctions expands the scope of fixed-point theory.
  • The study offers new insights into the endpoint behavior of set-valued functions.
  • The findings contribute to the theoretical understanding of multifunctions and their applications.