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.
Highlights
Geared up after the result of Kannan [2] in 1968, where he showed that discontinuous self-mapping has a unique fixed point, see Reference [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]
In 2014, Jleli et al [24,25] presented another important generalization of the Banach Contraction Principle, known as θ-contractions
Liu et al [26] discussed some important aspects of both F-contractions and θ-contractions
Summary
The process of generalizations and improvements of the Banach Contraction Principle [1] (1922). Piri et al [23] replaced assumption ( F3 ) by continuity of function F and proved a fixed point theorem, and in this way, presented the Wardowski theorem under weak conditions. Liu et al introduced a (Λ, Υ)-contraction, which contained both F-contractions and θ-contractions and established an important fixed point theorem extending corresponding theorems in References [22,23,24,25]. We prove a fixed point theorem, which generalizes the results of Liu et al [26]. Our presented results are subject to a binary relation
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
