Existence results of certain nonlinear polynomial and integral equations via $ \digamma $-contractive operators

Rosemary O. Ogbumba; Mohammed Shehu Shagari; Akbar Azam; Faryad Ali; Trad Alotaibi; Rosemary O. Ogbumba; Mohammed Shehu Shagari; Akbar Azam; Faryad Ali; Trad Alotaibi

doi:10.3934/math.20231466

AIMS Mathematics

2023, Volume 8, Issue 12: 28646-28669. doi: 10.3934/math.20231466

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Research article

Existence results of certain nonlinear polynomial and integral equations via $ \digamma $-contractive operators

1.
Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria
2.
Department of Mathematics, Grand Asian University, Sialkot, 7KM, Pasrur Road, Sialkot 51310, Pakistan
3.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi Arabia
4.
Department of Mathematics and Statistics, Taif University, Saudi Arabia

Received: 28 July 2023 Revised: 04 October 2023 Accepted: 16 October 2023 Published: 20 October 2023
MSC : 46J10, 47H10, 47H25, 54H25

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.
- $ \digamma $-contraction,
- $ G $-metric,
- fixed point,
- admissible mappings,
- nonlinear integral equation
Citation: Rosemary O. Ogbumba, Mohammed Shehu Shagari, Akbar Azam, Faryad Ali, Trad Alotaibi. Existence results of certain nonlinear polynomial and integral equations via $ \digamma $-contractive operators[J]. AIMS Mathematics, 2023, 8(12): 28646-28669. doi: 10.3934/math.20231466

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Abstract

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.

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