Existence results of certain nonlinear polynomial and integral equations via ϝ-contractive operators
In this manuscript, the concept of $ \digamma $-contraction is applied to extend the notion of Jaggi-Suzuki-type hybrid contraction in the framework of $ G $-metric space, which is termed Jaggi-Suzuki-type hybrid $ \digamma $-($ G $-$ \alpha $-$ \phi $)-contraction, and invariant point results which...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-10-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231466?viewType=HTML |
| _version_ | 1797635329893597184 |
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| author | Rosemary O. Ogbumba Mohammed Shehu Shagari Akbar Azam Faryad Ali Trad Alotaibi |
| author_facet | Rosemary O. Ogbumba Mohammed Shehu Shagari Akbar Azam Faryad Ali Trad Alotaibi |
| author_sort | Rosemary O. Ogbumba |
| collection | DOAJ |
| description | In this manuscript, the concept of $ \digamma $-contraction is applied to extend the notion of Jaggi-Suzuki-type hybrid contraction in the framework of $ G $-metric space, which is termed Jaggi-Suzuki-type hybrid $ \digamma $-($ G $-$ \alpha $-$ \phi $)-contraction, and invariant point results which cannot be inferred from their cognate ones in metric space are established. The results obtained herein provide a new direction and are generalizations of several well-known results in fixed point theory. An illustrative, comparative example is constructed to give credence to the results obtained. Furthermore, sufficient conditions for the existence and uniqueness of solutions of certain nonlinear polynomial and integral equations are established. For the purpose of future research, an open problem is highlighted regarding discretized population balance model whose solution may be investigated from the techniques proposed herein. |
| first_indexed | 2024-03-11T12:20:42Z |
| format | Article |
| id | doaj.art-54c4478c5eeb4f0ab22fc0b42daba37c |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T12:20:42Z |
| publishDate | 2023-10-01 |
| publisher | AIMS Press |
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| series | AIMS Mathematics |
| spelling | doaj.art-54c4478c5eeb4f0ab22fc0b42daba37c2023-11-07T01:28:46ZengAIMS PressAIMS Mathematics2473-69882023-10-01812286462866910.3934/math.20231466Existence results of certain nonlinear polynomial and integral equations via ϝ-contractive operatorsRosemary O. Ogbumba0Mohammed Shehu Shagari1Akbar Azam2Faryad Ali 3Trad Alotaibi41. Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria1. Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria2. Department of Mathematics, Grand Asian University, Sialkot, 7KM, Pasrur Road, Sialkot 51310, Pakistan3. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi Arabia4. Department of Mathematics and Statistics, Taif University, Saudi ArabiaIn this manuscript, the concept of $ \digamma $-contraction is applied to extend the notion of Jaggi-Suzuki-type hybrid contraction in the framework of $ G $-metric space, which is termed Jaggi-Suzuki-type hybrid $ \digamma $-($ G $-$ \alpha $-$ \phi $)-contraction, and invariant point results which cannot be inferred from their cognate ones in metric space are established. The results obtained herein provide a new direction and are generalizations of several well-known results in fixed point theory. An illustrative, comparative example is constructed to give credence to the results obtained. Furthermore, sufficient conditions for the existence and uniqueness of solutions of certain nonlinear polynomial and integral equations are established. For the purpose of future research, an open problem is highlighted regarding discretized population balance model whose solution may be investigated from the techniques proposed herein.https://www.aimspress.com/article/doi/10.3934/math.20231466?viewType=HTML$ \digamma $-contraction$ g $-metricfixed pointadmissible mappingsnonlinear integral equation |
| spellingShingle | Rosemary O. Ogbumba Mohammed Shehu Shagari Akbar Azam Faryad Ali Trad Alotaibi Existence results of certain nonlinear polynomial and integral equations via ϝ-contractive operators AIMS Mathematics $ \digamma $-contraction $ g $-metric fixed point admissible mappings nonlinear integral equation |
| title | Existence results of certain nonlinear polynomial and integral equations via ϝ-contractive operators |
| title_full | Existence results of certain nonlinear polynomial and integral equations via ϝ-contractive operators |
| title_fullStr | Existence results of certain nonlinear polynomial and integral equations via ϝ-contractive operators |
| title_full_unstemmed | Existence results of certain nonlinear polynomial and integral equations via ϝ-contractive operators |
| title_short | Existence results of certain nonlinear polynomial and integral equations via ϝ-contractive operators |
| title_sort | existence results of certain nonlinear polynomial and integral equations via ϝ contractive operators |
| topic | $ \digamma $-contraction $ g $-metric fixed point admissible mappings nonlinear integral equation |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231466?viewType=HTML |
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