A fixed point result for φ-contractions on b-metric spaces without the boundedness assumption

• Autorzy: Păcurar M.
• Języki publikacji: EN

Abstrakty

EN

Starting from a result in [V. Berinde,Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory (Preprint), "Babeş-Bolyai" University of Cluj-Napoca, 3 (1993), 3-9 ], we prove the existence and uniqueness of the fixed points for φ-contractions on b-metric spaces. We also build a theory of this fixed point result.

Słowa kluczowe

EN

b-metric space; phi-contraction; fixed point; well-posedness; limit shadowing property

PL

przestrzeń metryczna; punkt stały

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2010
• Tom: Nr 43
• Strony: 127--137
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Păcurar M.

• Department of Statistics Forecast and Mathematics Faculty of Economics and Bussiness Administration "Babes-Bolyai" University of Cluj-Napoca 58-60 T. Mihali St., 400591 Cluj-Napoca, Romania,

Bibliografia

• [1] Bakhtin I.A., The contraction principle in quasimetric spaces (Russian), Func.An., Unianowsk, Gos.Ped.Ins., 30(1989), 26-37.
• [2] Berinde V., Une generalization de critere du d’Alembert pour les series positives, Bul. St. Univ. Baia Mare, 7(1991), 21-26.
• [3] Berinde V., Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory (Preprint), ”Babeş-Bolyai” University of Cluj-Napoca, 3(1993), 3-9.
• [4] Berinde V., Sequences of operators and fixed points in quasimetric spaces, Stud. Univ. ”Babeş-Bolyai”, Math., 16(4)(1996), 23-27.
• [5] Berinde V., Contracţii generalizate şi aplicaţii, Editura Cub Press 22, Baia Mare, 1997.
• [6] Bourbaki N., Topologie gńérale, Herman, Paris, 1961.
• [7] Czerwik S., Nonlinear set-valued contraction mappings in b-metric spaces, Atti. Sem. Mat. Univ. Modena, 46(1998), 263-276.
• [8] Rus I.A., Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, 2001.
• [9] Rus I.A., Serban M.A., Some generalizations of a Cauchy lemma and applications, Topics in Mathematics, Computer Science and Philosophy. St. Cobzas (Ed.), Cluj University Press, Cluj-Napoca, (2008), 173-181.
• [10] Rus I.A., The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory, 9(2)(2008), 541-559.