Shagari, M. S., Oloche, P., & Noorwali, M. (2023). Solutions of mixed integral equations via hybrid contractions. Advances in the Theory of Nonlinear Analysis and Its Application, 7(5), 165–182.
- ISSN: 2587-2648
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Mohammed Shehu Shagaria, Paul Olocheb, Maha Noorwalic
aDepartment of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria
bDepartment of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria
cDepartment of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
This paper establishes certain new fixed point results for a class of contractions known as admissible hybrid (θ–ζ)-contraction within the context of rectangular metric space. The main contribution of this work is a straightforward unification of the notions of admissible mappings, θ-contractions, and the contraction mapping principle. As a result, several corollaries are inferred from the primary findings given here, some of which comprise previously disclosed concepts. An application of one of the obtained results is the proposal of new criteria for the existence and uniqueness of a solution to a mixed nonlinear fixed point problem, using Volterra-Fredholm integrals. Nontrivial analytical and numerical examples are given and compared with specific related articles to elucidate the underlying theoretical ideas.
Keywords: Fixed point; Metric space; θ-contraction; Nonlinear integral equation.
Shagari, M. S., Oloche, P., & Noorwali, M. (2023). Solutions of mixed integral equations via hybrid contractions. Advances in the Theory of Nonlinear Analysis and Its Application, 7(5), 165–182.