Mathematics (May 2019)

On (Λ,Υ,ℜ)-Contractions and Applications to Nonlinear Matrix Equations

  • Eskandar Ameer,
  • Muhammad Nazam,
  • Hassen Aydi,
  • Muhammad Arshad,
  • Nabil Mlaiki

DOI
https://doi.org/10.3390/math7050443
Journal volume & issue
Vol. 7, no. 5
p. 443

Abstract

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In this paper, we study the behavior of Λ , Υ , ℜ -contraction mappings under the effect of comparison functions and an arbitrary binary relation. We establish related common fixed point theorems. We explain the significance of our main theorem through examples and an application to a solution for the following nonlinear matrix equations: X = D + ∑ i = 1 n A i ∗ X A i − ∑ i = 1 n B i ∗ X B i X = D + ∑ i = 1 n A i ∗ γ X A i , where D is an Hermitian positive definite matrix, A i , B i are arbitrary p × p matrices and γ : H ( p ) → P ( p ) is an order preserving continuous map such that γ ( 0 ) = 0 . A numerical example is also presented to illustrate the theoretical findings.

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