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The Mechanics of (Poro-)Elastic Contractile Actomyosin Networks As a Model System of the Cell Cytoskeleton
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G-weak contraction in ordered cone rectangular metric spaces.

S K Malhotra1, J B Sharma, Satish Shukla

  • 1Department of Mathematics, Govt. S.G.S.P.G. College Ganj Basoda, Vidisha 464221, India.

Thescientificworldjournal
|June 20, 2013
PubMed
Summary
This summary is machine-generated.

This study proves common fixed-point theorems for ordered g-weak contractions in cone rectangular metric spaces. These findings extend existing results in metric spaces without requiring cone normality.

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Area of Science:

  • Fixed-point theory
  • Nonlinear analysis
  • Metric space topology

Background:

  • Ordered metric spaces provide a framework for studying inequalities and convergence.
  • Cone metric spaces and cone rectangular metric spaces generalize standard metric spaces using cones.
  • Fixed-point theorems are fundamental in analysis, with applications in differential equations and optimization.

Purpose of the Study:

  • To establish common fixed-point theorems for ordered g-weak contractions.
  • To investigate these theorems in cone rectangular metric spaces.
  • To relax the normality condition of the cone, broadening applicability.

Main Methods:

  • Utilizing the concept of ordered g-weak contractions.
  • Applying fixed-point iteration techniques within the specified metric space.
  • Developing theoretical proofs without assuming cone normality.

Main Results:

  • Proved common fixed-point theorems for ordered g-weak contractions in cone rectangular metric spaces.
  • Demonstrated that the normality of the cone is not a necessary condition.
  • Extended existing theorems from cone metric and cone rectangular spaces.

Conclusions:

  • The established theorems offer a more generalized framework for fixed-point results.
  • The findings contribute to the theory of metric spaces and fixed-point equations.
  • Illustrative examples confirm the validity and applicability of the new theorems.