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The technique for solving nonlinear matrix equations involving generalized contraction mappings via Ky Fan norms and Thompson metrics |
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| รหัสดีโอไอ | |
| Title | The technique for solving nonlinear matrix equations involving generalized contraction mappings via Ky Fan norms and Thompson metrics |
| Creator | Kanokwan Sawangsup |
| Contributor | Wutiphol Sintunavarat, Advisor |
| Publisher | Thammasat University |
| Publication Year | 2561 |
| Keyword | B-simulation function, Lower semicontinuous, Right upper semicontinuous, Thompson metric, Ky Fan norm |
| Abstract | The purpose of this dissertation is to investigate new contraction mappingsin metric spaces and b-metric spaces endowed with binary relations. Themain results of this dissertation are divided into two parts. In the first part, weimprove the notion of a Z-contraction mapping with respect to a b-simulation functionand also prove fixed point results on b-metric spaces endowed with only a transitiverelation. Our results can reduce to several important results in the past. Wealso introduce the concept of an (F,γ)R-contraction mapping, which is improvedfrom weaker conditions on F-contraction mappings in metric spaces endowed witha binary relation. We prove fixed point results for (F,γ)R -contraction mappingsand also furnish some examples to demonstrate the benefit of our main results.Furthermore, we introduce the new contraction namely (ψ , ∅, R)-contraction andprove the fixed point theorem for relation-theoretic (ψ , ∅, R)-contractions in a metricspace endowed with a T-orbital transitivity. We also give an example to showthe benefit of our theorems. In the last part, we extend and generalize Ran andReurings’s results to prove nonlinear matrix equations by giving new notions concerning b-simulation functions via Ky Fan norms. Also, we apply fixed point results for (F,γ)R contraction mappings and (ψ , ∅, R)-contraction mappings to prove the existence and uniqueness of a solution of some nonlinear matrix equations and we give some numerical examples to support some results of our applications. |
