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Tripled Fixed Points and Tripled Best Proximity Points in Modular Function Spaces
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DOI：10.3390/appliedmath5040167.png)
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Abstract
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We establish a modular-space framework for the study of tripled fixed points and tripled best proximity points. Under suitable assumptions on the underlying modular (convexity, the Delta 2 property, uniform continuity, and uniform convexity-type properties), we prove that Banach theorems guarantee the existence, uniqueness, and convergence of modular iterative schemes. In particular, we develop results for cyclic rho-Kannan contraction maps and pairs, showing that both tripled fixed points and tripled best proximity points arise uniquely and attract all iterative trajectories. An illustrative example in the space L2[0,1] with integral operators demonstrates the applicability of the theory and the predicted rate of convergence. These results extend classical fixed point methods to a broader modular setting and open the way for applications in nonlinear functional equations.
Keywords:
tripled fixed points
tripled best proximity points
modular function spaces
cyclic rho-Kannan contractions
Banach-type fixed-point theorems
Delta(2) property
integral operators
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0.7
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111
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