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Fixed Point Results for θ-Rational Contraction in Complete Metric Spaces

Year: 2026
Type: article
Abstract: This paper introduces and investigates a new family of nonlinear contraction-type mappings, termed θ-rational contractions, defined on complete metric spaces. This class is formulated through a function θ satisfying appropriate monotonicity and asymptotic regularity conditions and incorporates both rational-type expressions and power-type nonlinearities. The proposed framework unifies and extends several well-known contractive conditions, including the Jleli-Samet θ-contractions and the rational-type contractions of Dass-Gupta. A general fixed-point theorem is established, ensuring that a fixed point exists and is unique for θ-rational contractions, together with the convergence of the associated Picard iteration. A corollary shows that, by choosing θ(t) = e^t, the contractive condition reduces to a strict θ-contraction, thereby generalizing and strengthening the θ-contraction introduced by Jleli and Samet. Illustrative examples on both finite and continuous metric spaces are included to show the applicability of the established findings. Additionally, a common fixed-point result is established for commuting pairs of θ-rational contractions. These results highlight the flexibility of the θ-rational framework and offer a unified approach to a broad class of nonlinear contractive conditions.
DOI: 10.14419/hgz0m151
Language: Portuguese
Open Access status: diamond
OpenAlex ID: W7127045655
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