Fixed Point Theorems of Hegedus Contraction Mapping in Some Types of Distance Spaces


In the present paper, we prove some fixed point theorems of Hegedus contraction in some types of distance spaces, dislocated metric space, left dislocated metric space, right dislocated metric space and dislocated quasi-metric metric space which are generalized metrics spaces where self-distances are not necessarily zero.

Share and Cite:

Ahmed, M. , Zeyada, F. and Hassan, G. (2012) Fixed Point Theorems of Hegedus Contraction Mapping in Some Types of Distance Spaces. International Journal of Modern Nonlinear Theory and Application, 1, 93-96. doi: 10.4236/ijmnta.2012.13013.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] P. Hitzler, “Generalized Metrics Topology in Logic Programming Semantics,” Ph. D. Thesis, National University of Ireland (University College Cork), Dublin, 2001.
[2] P. Hitzler and A. K. Seda, “Dislocated Topologies,” Journal of Electrical Engineering, Vol. 51, No. 12/s, 2000, pp. 3-7.
[3] A. K. Seda, “Quasi Metrics and the Semantics of Logic Programs,” Fundamenta Informaticae, Vol. 29, No. 1, 1997, pp. 97-117.
[4] S. G. Matthews, “Metric Domains for Completeness,” Ph.D. Thesis, University of Warwick, Coventry, 1986.
[5] S. G. Matthews, “The Topology of Partial Metric Spaces,” Research Repodt 22, University of Warwick, Coventry, 1992, 19 p.
[6] P. Waszkiewicz, “The Local Triangle Axioms in Topology and Domain Theory,” Applied General Topology, Vol. 4, No. 1, 2003, pp. 47-70.
[7] P. Waszkiewicz, “Quantitative Continuous Domains,” Ph.D. Thesis, The Universiyy of Birminghham, Edgbaston, 2002.
[8] J. J. M. M. Rutten, “Elements of Generalized Ultrametric Domain Theory,” Theoretical Computer Science, Vol. 170, No. 1-2, 1996, pp. 349-381. doi:10.1016/S0304-3975(96)80711-0
[9] M. Hegedus, “Some Extension of Fixed Point Theorems,” Publications de l'Institut Mathématique (Beograd), Vol. 27. No. 41, 1980, pp. 77-82.

Copyright © 2021 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.