Unified relational-theoretic approach in metric-like spaces with an applicationopen access
- Authors
- Jain, R.; Nashine, H.K.; Lee, J.R.; Park, C.
- Issue Date
- 2021
- Publisher
- American Institute of Mathematical Sciences
- Keywords
- positive definite matrix; nonlinear matrix equation; metric-like space; relational metric space; fixed point
- Citation
- AIMS Mathematics, v.6, no.8, pp.8959 - 8977
- Indexed
- SCIE
SCOPUS
- Journal Title
- AIMS Mathematics
- Volume
- 6
- Number
- 8
- Start Page
- 8959
- End Page
- 8977
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/144067
- DOI
- 10.3934/math.2021520
- ISSN
- 2473-6988
- Abstract
- In this paper, we introduce a modified implicit relation and obtain some new fixed point results for σ-implicit type contractive conditions in relational metric-like spaces. We present some nontrivial examples to illustrative facts and compare our results with the related work. We also discuss sufficient conditions for the existence of a unique positive definite solution of the non-linear matrix equation U = D +∑m i=1 A∗iG(U)Ai, where D is an n × n Hermitian positive definite matrix, A1, A2, …, Am are n × n matrices, and G is a non-linear self-mapping of the set of all Hermitian matrices which is continuous in the trace norm. Finally, we discuss a couple of examples, convergence and error analysis, average CPU time analysis and visualization of solution in surface plot.
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