Generalized Ćirić’s contraction in quasi-metric spaces

Authors

  • Salvador Romaguera Instituto Universitario de Matemática Pura y Aplicada, Universitat Politécnica de Valéncia, 46022 Valencia, Spain

Keywords:

Ćirić’s contraction, quasi-metric space, complete, fixed point

Abstract

Inspired by a work from P. Kumam, N.V. Dung and K. Sitytithakerngkiet [Filomat 29 (2015), 1549–1556], we investigate the problem of obtaining fixed point results for generalizations of Ćirić’s contraction in the realm of quasi-metric spaces.

References

A. Amini-Harandi, D. Mihet, Quasi-contractive mappings in fuzzy metric spaces, Iran. J. Fuzzy Syst. 12 (2015), 147--153.

V. Berinde, General contractive fixed point theorems for Ciric-type almost contraction in metric spaces, Carpathian J. Math. 24 (2008), 10--19.

V. Berinde, Some remarks on a fixed point point theorem for Ciric-type almost

contractions, Carpathian J. Math. 25 (2009), 157--162.

L. Ciric, A generalization of Banach's contraction principle, Proc. Am. Math. Soc. 45 (1974), 267--273.

S. Cobzacs, Functional Analysis in Asymmetric Normed Spaces. Frontiers in Mathematics, Birkhauser/Springer Basel AG, Basel, Switzerland, 2013.

P. Fletcher, W.F. Lindgren, Quasi-Uniform Spaces, Marcel Dekker, New York, 1982.

L.M. Garcia-Raffi, S. Romaguera, M.P. Schellekens, Applications of the complexity space to the General

Probabilistic Divide and Conquer Algorithms. J. Math. Anal. Appl. 348 (2008), 346--355.

T.L. Hicks, Fixed point theorems for quasi-metric spaces, Math. Japon. 33 (1988), 231--236.

J. Jachymski, A contribution to fixed point theory in quasi-metric spaces, Publ. Math. Debrecen 43 (1993), 283--288.

E. Karapinar, Revisiting Ciric type nonunique fixed point theorems via interpolation, Appl. Gen. Topol. 22 (2021), 483--496.

J.C. Kelly, Bitopological spaces, Proc. London Math. Soc. 13 (1963), 71-89.

F. Kiany, A. Amini-Harandi, Fixed point theory for generalized Ciric quasi-contraction maps in metric spaces, Fixed Point Theory Appl. 2013, 2013:26.

P. Kumam, N.V. Dung, K. Sitytithakerngkiet, A generalization of Ciric fixed point theorems, Filomat 29 (2015), 1549--1556.

H.P.A. Kunzi, Nonsymmetric distances and their associated topologies: About

the origins of basic ideas in the area of asymmetric topology, In: Handbook of

the History of General Topology Vol. 3, C.E. Aull, R. Lowen, Eds. Kluwer, Dordrecht, 2001, pp. 853--968.

S.G. Matthews, Partial metric topology, Proc. 8th Summer Conference on

General Topology and Appl., Ann. New York Acad. Sci. 728, 1994, 183-197.

M. Noorwali, H.H. Alsulami, E. Karapinar, Some extensions of fixed point results over quasi-$JS$-spaces, J. Funct. Spaces (2016), 2016: 6963041.

D. Rakic, T. Dovsenovic, Z.D. Mitrovic, M. de la Sen,

S. Radenovic, Some fixed point theorems of Ciric type in fuzzy metric spaces, Mathematics 2020, 8, 297.

S. Romaguera, Contrations of Kannan-type and of Chatterjea-type on fuzzy quasi-metric spaces, Results Nonlinear Anal. 5 (2022), 347-359.

S. Romaguera, E. Checa, Continuity of contractive mappings on complete quasi-metric spaces, Math. Japon. 35 (1990), 137--139.

M. Schellekens, The Smyth completion: a common foundation for denonational

semantics and complexity analysis, Electron. Notes Theor. Comput. Sci. 1 (1995), 535-556.

A.K. Seda, Quasi-metrics and the semantics of logic programs, Fund. Inf. 29 (1997), 97--117.

A.K. Seda, P. Hitzler, Generalized distance functions in the theory of computation, Comput. J. 53 (2010), 443--464.

W.A. Wilson, On quasi-metric spaces, Amer. J. Math. 53 (1931), 675--684.

Downloads

Published

2023-02-05

Issue

Section

Articles