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

Author

Listed:
  • Eskandar Ameer

    (Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan
    Department of Mathematics, Taiz University, Taiz, Yemen)

  • Muhammad Nazam

    (Department of Mathematics, Allama Iqbal Open University, Islamabad 44000, Pakistan)

  • Hassen Aydi

    (Université de Sousse, Institut Supérieur d’Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia
    China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

  • Muhammad Arshad

    (Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad 44000, Pakistan)

  • Nabil Mlaiki

    (Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia)

Abstract

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.

Suggested Citation

  • Eskandar Ameer & Muhammad Nazam & Hassen Aydi & Muhammad Arshad & Nabil Mlaiki, 2019. "On (Λ,Υ,ℜ)-Contractions and Applications to Nonlinear Matrix Equations," Mathematics, MDPI, vol. 7(5), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:443-:d:232260
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