<i>PPF</i>-Dependent Fixed Point Results for Multi-Valued <i>ϕ</i>-<i>F</i>-Contractions in Banach Spaces and Applications
The solutions for many real life problems is obtained by interpreting the given problem mathematically in the form of <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
2019-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/11/1375 |
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| author | Mohammed M. M. Jaradat Babak Mohammadi Vahid Parvaneh Hassen Aydi Zead Mustafa |
| author_facet | Mohammed M. M. Jaradat Babak Mohammadi Vahid Parvaneh Hassen Aydi Zead Mustafa |
| author_sort | Mohammed M. M. Jaradat |
| collection | DOAJ |
| description | The solutions for many real life problems is obtained by interpreting the given problem mathematically in the form of <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 of such examples 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 paper, we initiate <inline-formula> <math display="inline"> <semantics> <mrow> <mi>ϕ</mi> <mo>−</mo> <mi>F</mi> </mrow> </semantics> </math> </inline-formula>-contractions and study the existence of PPF-dependent fixed points (fixed points for mappings having variant domains and ranges) for these related mappings in the Razumikhin class. Our theorems extend and improve the results of Hammad and De La Sen [Mathematics, 2019, 7, 52]. As applications of our PPF dependent fixed point results, we study the existence of solutions for delay differential equations (DDEs) which have numerous applications in population dynamics, bioscience problems and control engineering. |
| first_indexed | 2024-04-13T08:59:34Z |
| format | Article |
| id | doaj.art-1043b705fadb4a329def386e2721429b |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T08:59:34Z |
| publishDate | 2019-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-1043b705fadb4a329def386e2721429b2022-12-22T02:53:11ZengMDPI AGSymmetry2073-89942019-11-011111137510.3390/sym11111375sym11111375<i>PPF</i>-Dependent Fixed Point Results for Multi-Valued <i>ϕ</i>-<i>F</i>-Contractions in Banach Spaces and ApplicationsMohammed M. M. Jaradat0Babak Mohammadi1Vahid Parvaneh2Hassen Aydi3Zead Mustafa4Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, QatarDepartment of Mathematics, Marand Branch, Islamic Azad University, Marand, IranDepartment of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, IranUniversité de Sousse, Institut Supérieur d’Informatique et des Techniques de Communication, H. Sousse 4000, TunisiaDepartment of Mathematics, Statistics and Physics, Qatar University, Doha 2713, QatarThe solutions for many real life problems is obtained by interpreting the given problem mathematically in the form of <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 of such examples 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 paper, we initiate <inline-formula> <math display="inline"> <semantics> <mrow> <mi>ϕ</mi> <mo>−</mo> <mi>F</mi> </mrow> </semantics> </math> </inline-formula>-contractions and study the existence of PPF-dependent fixed points (fixed points for mappings having variant domains and ranges) for these related mappings in the Razumikhin class. Our theorems extend and improve the results of Hammad and De La Sen [Mathematics, 2019, 7, 52]. As applications of our PPF dependent fixed point results, we study the existence of solutions for delay differential equations (DDEs) which have numerous applications in population dynamics, bioscience problems and control engineering.https://www.mdpi.com/2073-8994/11/11/1375ppf-dependent fixed point<i>ϕ</i>-f-contractionsthe razumikhin classbanach space |
| spellingShingle | Mohammed M. M. Jaradat Babak Mohammadi Vahid Parvaneh Hassen Aydi Zead Mustafa <i>PPF</i>-Dependent Fixed Point Results for Multi-Valued <i>ϕ</i>-<i>F</i>-Contractions in Banach Spaces and Applications Symmetry ppf-dependent fixed point <i>ϕ</i>-f-contractions the razumikhin class banach space |
| title | <i>PPF</i>-Dependent Fixed Point Results for Multi-Valued <i>ϕ</i>-<i>F</i>-Contractions in Banach Spaces and Applications |
| title_full | <i>PPF</i>-Dependent Fixed Point Results for Multi-Valued <i>ϕ</i>-<i>F</i>-Contractions in Banach Spaces and Applications |
| title_fullStr | <i>PPF</i>-Dependent Fixed Point Results for Multi-Valued <i>ϕ</i>-<i>F</i>-Contractions in Banach Spaces and Applications |
| title_full_unstemmed | <i>PPF</i>-Dependent Fixed Point Results for Multi-Valued <i>ϕ</i>-<i>F</i>-Contractions in Banach Spaces and Applications |
| title_short | <i>PPF</i>-Dependent Fixed Point Results for Multi-Valued <i>ϕ</i>-<i>F</i>-Contractions in Banach Spaces and Applications |
| title_sort | i ppf i dependent fixed point results for multi valued i ϕ i i f i contractions in banach spaces and applications |
| topic | ppf-dependent fixed point <i>ϕ</i>-f-contractions the razumikhin class banach space |
| url | https://www.mdpi.com/2073-8994/11/11/1375 |
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