Existence of a solution for a nonlinear integral equation by nonlinear contractions involving simulation function in partially ordered metric space
In a recent paper, Khojasteh et al. presented a new collection of simulation functions, said Z-contraction. This form of contraction generalizes the Banach contraction and makes different types of nonlinear contractions. In this article, we discuss a pair of nonlinear operators that applies to a no...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2023-04-01
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| Series: | Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://zurnalai.vu.lt/nonlinear-analysis/article/view/32119 |
| _version_ | 1827958728190590976 |
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| author | Parvaneh Lo'Lo' Maryam Shams Manuel De la Sen |
| author_facet | Parvaneh Lo'Lo' Maryam Shams Manuel De la Sen |
| author_sort | Parvaneh Lo'Lo' |
| collection | DOAJ |
| description |
In a recent paper, Khojasteh et al. presented a new collection of simulation functions, said Z-contraction. This form of contraction generalizes the Banach contraction and makes different types of nonlinear contractions. In this article, we discuss a pair of nonlinear operators that applies to a nonlinear contraction including a simulation function in a partially ordered metric space. For this pair of operators with and without continuity, we derive some results about the coincidence and unique common fixed point. In the following, many known and dependent consequences in fixed point theory in a partially ordered metric space are deduced. As well, we furnish two interesting examples to explain our main consequences, so that one of them does not apply to the principle of Banach contraction. Finally, we use our consequences to create a solution for a particular type of nonlinear integral equation.
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| first_indexed | 2024-04-09T15:40:55Z |
| format | Article |
| id | doaj.art-84a1fc532f7440b0bd5b8c2be7494481 |
| institution | Directory Open Access Journal |
| issn | 1392-5113 2335-8963 |
| language | English |
| last_indexed | 2024-04-09T15:40:55Z |
| publishDate | 2023-04-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj.art-84a1fc532f7440b0bd5b8c2be74944812023-04-27T09:46:40ZengVilnius University PressNonlinear Analysis1392-51132335-89632023-04-012810.15388/namc.2023.28.32119Existence of a solution for a nonlinear integral equation by nonlinear contractions involving simulation function in partially ordered metric spaceParvaneh Lo'Lo'0Maryam Shams1Manuel De la Sen2Behbahan Khatam Alanbia University of TechnologyUniversity of ShahrekordUniversity of Basque Country In a recent paper, Khojasteh et al. presented a new collection of simulation functions, said Z-contraction. This form of contraction generalizes the Banach contraction and makes different types of nonlinear contractions. In this article, we discuss a pair of nonlinear operators that applies to a nonlinear contraction including a simulation function in a partially ordered metric space. For this pair of operators with and without continuity, we derive some results about the coincidence and unique common fixed point. In the following, many known and dependent consequences in fixed point theory in a partially ordered metric space are deduced. As well, we furnish two interesting examples to explain our main consequences, so that one of them does not apply to the principle of Banach contraction. Finally, we use our consequences to create a solution for a particular type of nonlinear integral equation. https://zurnalai.vu.lt/nonlinear-analysis/article/view/32119simulation functionscoincidence pointcompatiblepartially ordered metric spaceintegral equation |
| spellingShingle | Parvaneh Lo'Lo' Maryam Shams Manuel De la Sen Existence of a solution for a nonlinear integral equation by nonlinear contractions involving simulation function in partially ordered metric space Nonlinear Analysis simulation functions coincidence point compatible partially ordered metric space integral equation |
| title | Existence of a solution for a nonlinear integral equation by nonlinear contractions involving simulation function in partially ordered metric space |
| title_full | Existence of a solution for a nonlinear integral equation by nonlinear contractions involving simulation function in partially ordered metric space |
| title_fullStr | Existence of a solution for a nonlinear integral equation by nonlinear contractions involving simulation function in partially ordered metric space |
| title_full_unstemmed | Existence of a solution for a nonlinear integral equation by nonlinear contractions involving simulation function in partially ordered metric space |
| title_short | Existence of a solution for a nonlinear integral equation by nonlinear contractions involving simulation function in partially ordered metric space |
| title_sort | existence of a solution for a nonlinear integral equation by nonlinear contractions involving simulation function in partially ordered metric space |
| topic | simulation functions coincidence point compatible partially ordered metric space integral equation |
| url | https://zurnalai.vu.lt/nonlinear-analysis/article/view/32119 |
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