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Common fixed point theorems for -contraction in b-metric-like spaces.

Dakun Yu1, Chunfang Chen2, Hong Wang2

  • 11School of Communication and Information Engineering, Shanghai University, Shanghai, P.R. China.

Journal of Inequalities and Applications
|March 7, 2019
PubMed
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This study introduces a new mathematical concept, the lambda-contraction, and explores its fixed-point theorems within b-metric-like spaces. Results are supported by an example and an application.

Keywords:
Common fixed pointb-metric-like spaces

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Area of Science:

  • Mathematics
  • Fixed-point theory
  • Metric spaces

Background:

  • Fixed-point theorems are fundamental in various mathematical fields.
  • Exploring new types of contractions can extend existing theories.
  • b-metric-like spaces offer a generalized framework for metric spaces.

Purpose of the Study:

  • To introduce and define the concept of lambda-contraction.
  • To investigate and establish fixed-point theorems for lambda-contractions in b-metric-like spaces.
  • To demonstrate the validity of the theoretical results with a practical example and application.

Main Methods:

  • Definition of lambda-contraction.
  • Application of fixed-point theorems in the context of b-metric-like spaces.
  • Illustrative example and proposed application.

Main Results:

  • Establishment of novel fixed-point theorems for lambda-contractions.
  • Demonstration of the existence and uniqueness of fixed points under specific conditions.
  • Validation of theoretical findings through a supporting example.

Conclusions:

  • The concept of lambda-contraction provides a valuable extension in fixed-point theory.
  • The established theorems are applicable and extend existing results in generalized metric spaces.
  • The proposed application highlights the practical relevance of lambda-contractions.