000144750 001__ 144750 000144750 005__ 20250923084418.0 000144750 0247_ $$2doi$$a10.3390/axioms13070474 000144750 0248_ $$2sideral$$a139581 000144750 037__ $$aART-2024-139581 000144750 041__ $$aeng 000144750 100__ $$0(orcid)0000-0003-4847-0493$$aNavascués, María A. 000144750 245__ $$aStability of Fixed Points of Partial Contractivities and Fractal Surfaces 000144750 260__ $$c2024 000144750 5060_ $$aAccess copy available to the general public$$fUnrestricted 000144750 5203_ $$aIn this paper, a large class of contractions is studied that contains Banach and Matkowski maps as particular cases. Sufficient conditions for the existence of fixed points are proposed in the framework of b-metric spaces. The convergence and stability of the Picard iterations are analyzed, giving error estimates for the fixed-point approximation. Afterwards, the iteration proposed by Kirk in 1971 is considered, studying its convergence, stability, and error estimates in the context of a quasi-normed space. The properties proved can be applied to other types of contractions, since the self-maps defined contain many others as particular cases. For instance, if the underlying set is a metric space, the contractions of type Kannan, Chatterjea, Zamfirescu, Ćirić, and Reich are included in the class of contractivities studied in this paper. These findings are applied to the construction of fractal surfaces on Banach algebras, and the definition of two-variable frames composed of fractal mappings with values in abstract Hilbert spaces. 000144750 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000144750 590__ $$a1.6$$b2024 000144750 591__ $$aMATHEMATICS, APPLIED$$b98 / 343 = 0.286$$c2024$$dQ2$$eT1 000144750 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000144750 773__ $$g13, 7 (2024), 474 [17 pp.]$$pAxioms$$tAxioms$$x2075-1680 000144750 8564_ $$s319270$$uhttps://zaguan.unizar.es/record/144750/files/texto_completo.pdf$$yVersión publicada 000144750 8564_ $$s2543113$$uhttps://zaguan.unizar.es/record/144750/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000144750 909CO $$ooai:zaguan.unizar.es:144750$$particulos$$pdriver 000144750 951__ $$a2025-09-22-14:34:02 000144750 980__ $$aARTICLE