Common Fixed Point Results of Set Valued Maps for <i>A<sub>φ</sub></i>-Contraction and Generalized <i>ϕ</i>-Type Weak Contraction
The solutions for many real life problems may be obtained by interpreting the given problem mathematically in the form <inline-formula> <math display="inline"> <semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/7/894 |
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| author | Murchana Neog Mohammed M. M. Jaradat Pradip Debnath |
| author_facet | Murchana Neog Mohammed M. M. Jaradat Pradip Debnath |
| author_sort | Murchana Neog |
| collection | DOAJ |
| description | The solutions for many real life problems may be obtained by interpreting the given problem mathematically in the form <inline-formula> <math display="inline"> <semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <mi>x</mi> </mrow> </semantics> </math> </inline-formula>. One such example is that of the famous Borsuk−Ulam theorem in which, using some fixed point argument, it can be guaranteed that at any given time we can find two diametrically opposite places in a planet with same temperature. Thus, the correlation of symmetry is inherent in the study of fixed point theory. In this article, some new results concerning coincidence and a common fixed point for an <inline-formula> <math display="inline"> <semantics> <msub> <mi>A</mi> <mi>φ</mi> </msub> </semantics> </math> </inline-formula>-contraction and a generalized <inline-formula> <math display="inline"> <semantics> <mi>ϕ</mi> </semantics> </math> </inline-formula>-type weak contraction are established. We prove our results for set valued maps without using continuity of the corresponding maps and completeness of the relevant space. Our results generalize and extend several existing results. Some new examples are given to demonstrate the generality and non-triviality of our results. |
| first_indexed | 2024-04-14T05:17:41Z |
| format | Article |
| id | doaj.art-9a27b74f671c4545a2ec07addf4df2ac |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-14T05:17:41Z |
| publishDate | 2019-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-9a27b74f671c4545a2ec07addf4df2ac2022-12-22T02:10:18ZengMDPI AGSymmetry2073-89942019-07-0111789410.3390/sym11070894sym11070894Common Fixed Point Results of Set Valued Maps for <i>A<sub>φ</sub></i>-Contraction and Generalized <i>ϕ</i>-Type Weak ContractionMurchana Neog0Mohammed M. M. Jaradat1Pradip Debnath2Department of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli, Arunachal Pradesh 791109, IndiaDepartment of Mathematics, Statistics and Physics, Qatar University, Doha P.O. Box 2713, QatarDepartment of Applied Science and Humanities, Assam University, Silchar, Cachar, Assam 788011, IndiaThe solutions for many real life problems may be obtained by interpreting the given problem mathematically in the form <inline-formula> <math display="inline"> <semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <mi>x</mi> </mrow> </semantics> </math> </inline-formula>. One such example is that of the famous Borsuk−Ulam theorem in which, using some fixed point argument, it can be guaranteed that at any given time we can find two diametrically opposite places in a planet with same temperature. Thus, the correlation of symmetry is inherent in the study of fixed point theory. In this article, some new results concerning coincidence and a common fixed point for an <inline-formula> <math display="inline"> <semantics> <msub> <mi>A</mi> <mi>φ</mi> </msub> </semantics> </math> </inline-formula>-contraction and a generalized <inline-formula> <math display="inline"> <semantics> <mi>ϕ</mi> </semantics> </math> </inline-formula>-type weak contraction are established. We prove our results for set valued maps without using continuity of the corresponding maps and completeness of the relevant space. Our results generalize and extend several existing results. Some new examples are given to demonstrate the generality and non-triviality of our results.https://www.mdpi.com/2073-8994/11/7/894common fixed point<i>A<sub>φ</sub></i>-contractiongeneralized <i>ϕ</i>-type weak contractioncommon property (<i>EA</i>) |
| spellingShingle | Murchana Neog Mohammed M. M. Jaradat Pradip Debnath Common Fixed Point Results of Set Valued Maps for <i>A<sub>φ</sub></i>-Contraction and Generalized <i>ϕ</i>-Type Weak Contraction Symmetry common fixed point <i>A<sub>φ</sub></i>-contraction generalized <i>ϕ</i>-type weak contraction common property (<i>EA</i>) |
| title | Common Fixed Point Results of Set Valued Maps for <i>A<sub>φ</sub></i>-Contraction and Generalized <i>ϕ</i>-Type Weak Contraction |
| title_full | Common Fixed Point Results of Set Valued Maps for <i>A<sub>φ</sub></i>-Contraction and Generalized <i>ϕ</i>-Type Weak Contraction |
| title_fullStr | Common Fixed Point Results of Set Valued Maps for <i>A<sub>φ</sub></i>-Contraction and Generalized <i>ϕ</i>-Type Weak Contraction |
| title_full_unstemmed | Common Fixed Point Results of Set Valued Maps for <i>A<sub>φ</sub></i>-Contraction and Generalized <i>ϕ</i>-Type Weak Contraction |
| title_short | Common Fixed Point Results of Set Valued Maps for <i>A<sub>φ</sub></i>-Contraction and Generalized <i>ϕ</i>-Type Weak Contraction |
| title_sort | common fixed point results of set valued maps for i a sub φ sub i contraction and generalized i ϕ i type weak contraction |
| topic | common fixed point <i>A<sub>φ</sub></i>-contraction generalized <i>ϕ</i>-type weak contraction common property (<i>EA</i>) |
| url | https://www.mdpi.com/2073-8994/11/7/894 |
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