Convergence results for cyclic-orbital contraction in a more generalized setting with application

Haroon Ahmad; Sana Shahab; Wael F. M. Mobarak; Ashit Kumar Dutta; Yasser M. Abolelmagd; Zaffar Ahmed Shaikh; Mohd Anjum; Haroon Ahmad; Sana Shahab; Wael F. M. Mobarak; Ashit Kumar Dutta; Yasser M. Abolelmagd; Zaffar Ahmed Shaikh; Mohd Anjum

doi:10.3934/math.2024751

AIMS Mathematics

2024, Volume 9, Issue 6: 15543-15558. doi: 10.3934/math.2024751

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Research article

Convergence results for cyclic-orbital contraction in a more generalized setting with application

1.
Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan
2.
Department of Business Administration, College of Business Administration, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
3.
Civil Engineering Department, College of Engineering, University of Business and Technology, Jeddah 21448, Saudi Arabia
4.
Engineering Mathematics Department, Alexandria University, Alexandria, Egypt
5.
Department of Computer Science and Information Systems, College of Applied Sciences, AlMaarefa University, Ad Diriyah, Riyadh 13713, Kingdom of Saudi Arabia
6.
Department of Computer Science and Information Technology, Benazir Bhutto Shaheed University Lyari, Karachi 75660, Pakistan
7.
Department of Computer Engineering, Aligarh Muslim University, Aligarh 202002, India

Received: 02 March 2024 Revised: 22 April 2024 Accepted: 24 April 2024 Published: 29 April 2024
MSC : 34B15, 41A65, 46B20, 47H10

In the realm of double-controlled metric-type spaces, we investigated obtaining fixed points using the application of cyclic orbital contractive conditions. Diverging from conventional approaches utilized in standard metric spaces, our technique took a unique route due to the unique features of our structure. We demonstrated the significance of our outcomes through exemplary cases, clarifying the breadth of our results through comprehensive investigations. Significantly, our work not only improved and broadened earlier findings in the literature, but also offered unique notions that were discussed in our explanatory notes. Towards the end of our inquiry, we used insights obtained from previous discoveries to develop a second-order differential equation. This equation was an effective tool for dealing with the second class of Fredholm integral problems. In conclusion, this investigation extended our examination of double-controlled metric type spaces by providing new insights on fixed point theory, expanding on prior debates and building a substantial road towards solving a class of integral equations.
- double controlled metric type space,
- fixed point,
- cyclic contraction,
- $ \digamma $-type contractive mappings
Citation: Haroon Ahmad, Sana Shahab, Wael F. M. Mobarak, Ashit Kumar Dutta, Yasser M. Abolelmagd, Zaffar Ahmed Shaikh, Mohd Anjum. Convergence results for cyclic-orbital contraction in a more generalized setting with application[J]. AIMS Mathematics, 2024, 9(6): 15543-15558. doi: 10.3934/math.2024751

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Abstract

In the realm of double-controlled metric-type spaces, we investigated obtaining fixed points using the application of cyclic orbital contractive conditions. Diverging from conventional approaches utilized in standard metric spaces, our technique took a unique route due to the unique features of our structure. We demonstrated the significance of our outcomes through exemplary cases, clarifying the breadth of our results through comprehensive investigations. Significantly, our work not only improved and broadened earlier findings in the literature, but also offered unique notions that were discussed in our explanatory notes. Towards the end of our inquiry, we used insights obtained from previous discoveries to develop a second-order differential equation. This equation was an effective tool for dealing with the second class of Fredholm integral problems. In conclusion, this investigation extended our examination of double-controlled metric type spaces by providing new insights on fixed point theory, expanding on prior debates and building a substantial road towards solving a class of integral equations.

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