Best Proximity Point Results for Generalized Θ-Contractions and Application to Matrix Equations
In this paper, we introduce the notion of C ´ iri c ´ type α - ψ - Θ -contraction and prove best proximity point results in the context of complete metric spaces. Moreover, we prove some best proximity point results in partially ordered complete metric spaces through our m...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-01-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/11/1/93 |
| _version_ | 1818040792479956992 |
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| author | Zhenhua Ma Azhar Hussain Muhammad Adeel Nawab Hussain Ekrem Savas |
| author_facet | Zhenhua Ma Azhar Hussain Muhammad Adeel Nawab Hussain Ekrem Savas |
| author_sort | Zhenhua Ma |
| collection | DOAJ |
| description | In this paper, we introduce the notion of C ´ iri c ´ type α - ψ - Θ -contraction and prove best proximity point results in the context of complete metric spaces. Moreover, we prove some best proximity point results in partially ordered complete metric spaces through our main results. As a consequence, we obtain some fixed point results for such contraction in complete metric and partially ordered complete metric spaces. Examples are given to illustrate the results obtained. Moreover, we present the existence of a positive definite solution of nonlinear matrix equation X = Q + ∑ i = 1 m A i * γ ( X ) A i and give a numerical example. |
| first_indexed | 2024-12-10T08:20:09Z |
| format | Article |
| id | doaj.art-7ab1b1f5c2f3416994216d1e2ccaeb43 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-12-10T08:20:09Z |
| publishDate | 2019-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-7ab1b1f5c2f3416994216d1e2ccaeb432022-12-22T01:56:21ZengMDPI AGSymmetry2073-89942019-01-011119310.3390/sym11010093sym11010093Best Proximity Point Results for Generalized Θ-Contractions and Application to Matrix EquationsZhenhua Ma0Azhar Hussain1Muhammad Adeel2Nawab Hussain3Ekrem Savas4Department of Mathematics and Physics, Hebei University of Architecture, Zhangjiakou 075024, ChinaDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Usak University, Usak 64100, TurkeyIn this paper, we introduce the notion of C ´ iri c ´ type α - ψ - Θ -contraction and prove best proximity point results in the context of complete metric spaces. Moreover, we prove some best proximity point results in partially ordered complete metric spaces through our main results. As a consequence, we obtain some fixed point results for such contraction in complete metric and partially ordered complete metric spaces. Examples are given to illustrate the results obtained. Moreover, we present the existence of a positive definite solution of nonlinear matrix equation X = Q + ∑ i = 1 m A i * γ ( X ) A i and give a numerical example.http://www.mdpi.com/2073-8994/11/1/93Θ-contractionα-ψ-contractionbest proximity point |
| spellingShingle | Zhenhua Ma Azhar Hussain Muhammad Adeel Nawab Hussain Ekrem Savas Best Proximity Point Results for Generalized Θ-Contractions and Application to Matrix Equations Symmetry Θ-contraction α-ψ-contraction best proximity point |
| title | Best Proximity Point Results for Generalized Θ-Contractions and Application to Matrix Equations |
| title_full | Best Proximity Point Results for Generalized Θ-Contractions and Application to Matrix Equations |
| title_fullStr | Best Proximity Point Results for Generalized Θ-Contractions and Application to Matrix Equations |
| title_full_unstemmed | Best Proximity Point Results for Generalized Θ-Contractions and Application to Matrix Equations |
| title_short | Best Proximity Point Results for Generalized Θ-Contractions and Application to Matrix Equations |
| title_sort | best proximity point results for generalized θ contractions and application to matrix equations |
| topic | Θ-contraction α-ψ-contraction best proximity point |
| url | http://www.mdpi.com/2073-8994/11/1/93 |
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