Some <em>φ</em>-Fixed Point Results for (<em>F</em>,<em>φ</em>,<em>α</em>-<em>ψ</em>)-Contractive Type Mappings with Applications
In this paper, we introduce the notions of (<i>F</i>,<inline-formula> <math display="inline"> <semantics> <mi>φ</mi> </semantics> </math> </inline-formula>,<inline-formula> <math display="inline"> <semanti...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/2/122 |
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| author | Mohammad Imdad Abdur Rauf Khan Hayel N. Saleh Waleed M. Alfaqih |
| author_facet | Mohammad Imdad Abdur Rauf Khan Hayel N. Saleh Waleed M. Alfaqih |
| author_sort | Mohammad Imdad |
| collection | DOAJ |
| description | In this paper, we introduce the notions of (<i>F</i>,<inline-formula> <math display="inline"> <semantics> <mi>φ</mi> </semantics> </math> </inline-formula>,<inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-<inline-formula> <math display="inline"> <semantics> <mi>ψ</mi> </semantics> </math> </inline-formula>)-contractions and (<i>F</i>,<inline-formula> <math display="inline"> <semantics> <mi>φ</mi> </semantics> </math> </inline-formula>,<inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-<inline-formula> <math display="inline"> <semantics> <mi>ψ</mi> </semantics> </math> </inline-formula>)-weak contractions in metric spaces and utilize the same to prove some existence and uniqueness <inline-formula> <math display="inline"> <semantics> <mi>φ</mi> </semantics> </math> </inline-formula>-fixed point results. Some illustrative examples are given to demonstrate the usefulness and effectiveness of our results. As applications, we deduce some fixed point theorems in partial metric spaces besides proving an existence result on the solution of nonlinear differential equations. Our results extend, generalize and improve some relevant results of the existing literature. |
| first_indexed | 2024-04-14T03:15:34Z |
| format | Article |
| id | doaj.art-23f0ce49525c498c9ca66027ae4eb8a3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-14T03:15:34Z |
| publishDate | 2019-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-23f0ce49525c498c9ca66027ae4eb8a32022-12-22T02:15:29ZengMDPI AGMathematics2227-73902019-01-017212210.3390/math7020122math7020122Some <em>φ</em>-Fixed Point Results for (<em>F</em>,<em>φ</em>,<em>α</em>-<em>ψ</em>)-Contractive Type Mappings with ApplicationsMohammad Imdad0Abdur Rauf Khan1Hayel N. Saleh2Waleed M. Alfaqih3Department of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Applied Sciences, University Polytechnic, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Hajjah University, Hajjah, YemenIn this paper, we introduce the notions of (<i>F</i>,<inline-formula> <math display="inline"> <semantics> <mi>φ</mi> </semantics> </math> </inline-formula>,<inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-<inline-formula> <math display="inline"> <semantics> <mi>ψ</mi> </semantics> </math> </inline-formula>)-contractions and (<i>F</i>,<inline-formula> <math display="inline"> <semantics> <mi>φ</mi> </semantics> </math> </inline-formula>,<inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-<inline-formula> <math display="inline"> <semantics> <mi>ψ</mi> </semantics> </math> </inline-formula>)-weak contractions in metric spaces and utilize the same to prove some existence and uniqueness <inline-formula> <math display="inline"> <semantics> <mi>φ</mi> </semantics> </math> </inline-formula>-fixed point results. Some illustrative examples are given to demonstrate the usefulness and effectiveness of our results. As applications, we deduce some fixed point theorems in partial metric spaces besides proving an existence result on the solution of nonlinear differential equations. Our results extend, generalize and improve some relevant results of the existing literature.https://www.mdpi.com/2227-7390/7/2/122φ-fixed pointα-ψ-contraction mappings(F,φ,α-ψ)-contraction mappings(F,φ,α-ψ)-weak contraction mappingspartial metric spaces |
| spellingShingle | Mohammad Imdad Abdur Rauf Khan Hayel N. Saleh Waleed M. Alfaqih Some <em>φ</em>-Fixed Point Results for (<em>F</em>,<em>φ</em>,<em>α</em>-<em>ψ</em>)-Contractive Type Mappings with Applications Mathematics φ-fixed point α-ψ-contraction mappings (F,φ,α-ψ)-contraction mappings (F,φ,α-ψ)-weak contraction mappings partial metric spaces |
| title | Some <em>φ</em>-Fixed Point Results for (<em>F</em>,<em>φ</em>,<em>α</em>-<em>ψ</em>)-Contractive Type Mappings with Applications |
| title_full | Some <em>φ</em>-Fixed Point Results for (<em>F</em>,<em>φ</em>,<em>α</em>-<em>ψ</em>)-Contractive Type Mappings with Applications |
| title_fullStr | Some <em>φ</em>-Fixed Point Results for (<em>F</em>,<em>φ</em>,<em>α</em>-<em>ψ</em>)-Contractive Type Mappings with Applications |
| title_full_unstemmed | Some <em>φ</em>-Fixed Point Results for (<em>F</em>,<em>φ</em>,<em>α</em>-<em>ψ</em>)-Contractive Type Mappings with Applications |
| title_short | Some <em>φ</em>-Fixed Point Results for (<em>F</em>,<em>φ</em>,<em>α</em>-<em>ψ</em>)-Contractive Type Mappings with Applications |
| title_sort | some em φ em fixed point results for em f em em φ em em α em em ψ em contractive type mappings with applications |
| topic | φ-fixed point α-ψ-contraction mappings (F,φ,α-ψ)-contraction mappings (F,φ,α-ψ)-weak contraction mappings partial metric spaces |
| url | https://www.mdpi.com/2227-7390/7/2/122 |
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