04-Faculty of Exact Sciences and Natural and Life Sciences

كلية العلوم الدقيقة وعلوم الطبيعة والحياة

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Fixed Point Results in Elliptic-Valued Metric Spaces with Applications
(Larbi Tebessi University-Tebessa, 2026-06-02) LEMITA, Samira; BERRAH, Khaled
This work is devoted to the study of fixed point theorems for several classes of con- tractive mappings in elliptic-valued metric spaces (E-VMS) and in the newly in- troduced extended elliptic-valued b-metric spaces (extended E-VMS). Building on the recent work of Özturk and Alamri–Özturk–Bota, where distances take values in the field Ep = {v + iw : v, w ∈ R, i2 = p < 0} of elliptic numbers, we establish ex- istence and uniqueness theorems of Kannan, Chatterjea and Dass–Gupta rational type, together with a closed-ball version of the latter, and we then extend each result to extended E-VMS by replacing the constant of the triangle inequality with a control function θ : W × W → [1, ∞). As an application, we prove the existence of solutions of the Urysohn integral equation in both frameworks, and we recover the corresponding theorems in complex-valued metric spaces as the special case p = −1. The proofs rely on the Picard iteration, a careful use of the elliptic norm, and the completeness of the ambient space; explicit examples and remarks illustrate the abstract results and clarify the relationships between the different contraction classes.