ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 18 (2023), 317 -- 328
This work is licensed under a Creative Commons Attribution 4.0 International License.
NEW DYNAMIC FIXED POINT RESULTS IN MENGER SPACES
Besma Laouadi, Liliana Guran, Taki Eddine Oussaeif, Leila Benaoua and Ioana Camelia Tişe
Abstract. The objective of this paper is to generalize
and improve some results in fixed point theorems in both complete metric space
and Menger space. These results are generalizations of the analogous ones recently
proved by Khojasteh [5], Demma [1],
Yildirim [13],
where we establish a dynamic information about their other fixed points if there exist i.e the distance between two fixed point in case of metric space and their equivalent in probabilistic metric space. Some illustrative examples are furnished, which demonstrate the validity of the hypotheses.
As an application to our main result, we derive a uniqueness fixed point theorem for a self-mapping under strong conditions.
2020 Mathematics Subject Classification: Primary 47H10; Secondary 54H25.
Keywords: Fixed point; Menger space; Picard sequence; Complete metric space.
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Besma Laouadi, Taki Eddine Oussaeif, Leila Benaoua
Dynamic Systems and Controls Laboratory (DSC),
Department of Mathematics, Larbi Ben M'hidi University,
Oum El Bouaghi, Algeria.
E-mails: laouadi.besma@univ-oeb.dz, taki_maths@live.fr, benaoualeila@gmail.com
Liliana Guran
Department of Hospitality Services, Babeş-Bolyai University,
Horea Street, no. 7, 400174, Cluj-Napoca, Romania.
E-mail: liliana.guran@ubbcluj.ro
Ioana Camelia Tişe
Department of Mathematics, Babeş-Bolyai University,
M. Kogălniceanu Street, no. 1, 400084, Cluj-Napoca, Romania.
E-mail: ti_camelia@yahoo.com