Abstract
Objectives: To prove fixed point theorem for non-self mappings of rational type in -multiplicative metric spaces and apply the theorem to solve integral equations. Method: Multiplicative metrically convex is defined in the context of - multiplicative metric spaces to prove fixed point theorems for pairs of non-self mappings using rational type contraction. Findings: The theorem demonstrates that under certain rational type contraction, a unique fixed point exists for non-self mappings in -multiplicative metric spaces. Applications of integral equations shown improved convergence and solution accuracy. Novelty: First fixed point theorem for non-self mappings in -multiplicative metric spaces, introducing a new approach to solving Volterra-Hammerstein integral equations. 2020 Mathematics Subject Classification: 47H10, 54H25. Keywords: Coincidence Point, Nonself Mappings, Rational Type contraction, b-Multiplicative Metric Spaces (b-m ́ms), Volterra-Hammerstein integral equations
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