Abstract
The purpose of this paper is to discuss some problems of the fixed point theory for non-self operators on \({\mathbb R}^m_+\)-metric spaces. The results complement and extend some known results given in the paper: A. Chis-Novac, R. Precup, I.A. Rus, Data dependence of fixed points for non-self generalized contractions, Fixed Point Theory, 10(2009), No. 1, 73–87.
Authors
Diana Otrocol
Technical University of Cluj-Napoca, Department of Mathematics, Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania
Veronica Ilea
Babes–Bolyai University, Department of Mathematics, Cluj-Napoca, Romania
Adela Novac
Technical University of Cluj-Napoca, Department of Mathematics, Cluj-Napoca, Romania
Keywords
\({\mathbb R}^m_+\)–metric spaces; fixed point; Picard operator; non-self operator; data dependence of the fixed point.
Paper coordinates
D. Otrocol, V. Ilea, A. Novac, Fixed point results for non-self operators R₊m-metric spaces, Fixed Point Theory, 26 (2025) no. 1, 177-188,
https://doi.org/10.24193/fpt-ro.2025.1.10
freely available at the publisher
About this paper
Journal
Fixed Point Theory
Publisher Name
House of the Book of Science Cluj-Napoca, Romania
Print ISSN
1583-5022
Online ISSN
2066-9208
google scholar link
[1] V. Berinde, S. Maruster, I.A. Rus, Saturated contraction principles for non-self operators, generalizations and applications, Filomat, 31(11)(2017), 3391-3406.
[2] V. Berinde, A. Petru¸sel, I.A. Rus, Remarks on the terminology of the mappings in fixed point iterative methods in metric space, Fixed Point Theory, 24(2023), no. 2, 525–540.
[3] A. Chis-Novac, R. Precup, I.A. Rus, Data dependence of fixed points for non-self generalized contractions, Fixed Point Theory, 10(2009), no. 1, 73–87.
[4] M. Frigon, Fixed point and continuation results for contractions and Gauge spaces, Banach Center Publications, 77(2007), 89-114.
[5] V. Ilea, A. Novac, D. Otrocol, Fixed point results for weakly Picard non-self operators on Rm+ -metric spaces, sent for publication.
[6] V. Ilea, D. Otrocol, I.A. Rus, M.A. Serban, Applications of fibre contraction principle to some classes of functional integral equations, Fixed Point Theory, 23(2022), no. 1, 279-292.
[7] J.M. Ortega, W.C. Reinboldt, On a class of approximative iterative processes, Arch. Rat. Mech. Anal., 23(1967), 352-365.
[8] I.A. Rus, Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, 2001.
[9] I.A. Rus, Picard operators and applications, Scientiae Mathematicae Japonicae, 58(2003), no.1, 191-219.
[10] I.A. Rus, Metric space with fixed point property with respect to contractions, Stud. Univ. BabesBolyai Math., 51(2006), no. 3, 115-121.
[11] I.A. Rus, The theory of a metrical fixed point theorem: Theoretical and applicative relevances, Fixed Point Theory, 9(2008), no. 2, 541-559.
[12] I.A. Rus, Some variants of contraction principle, generalizations and applications, Stud. Univ. Babe¸s-Bolyai Math. 61(2016), no. 3, 343–358.
[13] I.A. Rus, A. Petrusel, M.A. Serban, Weakly Picard operators: Equivalent definitions, applications and open problems, Fixed Point Theory, 7(2006), no. 1, 3-22.
[14] I.A. Rus, M.A. Serban, Some generalizations of a Cauchy lemma and applications, Topics in Mathematics, Computer Science and Philosophy, Presa Universitar˘a Clujeana, 2008, 173-181.
[15] M.A. Serban, Fibre contraction theorem in generalized metric spaces, Automat. Comput. Appl. Math., 16(2007), no. 1, 139-144.
[16] M.A. Serban, Saturated fibre contraction principle, Fixed Point Theory, 18(2017), no. 2, 729–740.