Fixed point on generalized dislocated metric spaces

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, Al-Zulfi, Majmaah University, Majmaah, 11952, Saudi Arabia

2 Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt

3 Centre for Mathematics and Statistical Sciences, Lahore School of Economics, Lahore 53200, Pakistan

4 Department of Mathematics, Faculty of Science, Port Said University, Port Said, Egypt

Abstract

In the present paper, we introduce new types of convergence of a sequence in left dislocated and right dislocated metric spaces. Also, we generalize the Banach contraction principle in these newly defined generalized metric spaces.

Keywords

[1] I. Beg, M. Arshad and A. Shoaib, Fixed point on a closed ball in ordered dislocated quasi metric spaces, Fixed
Point Theory, 16(2) (2015) 195–206.
[2] M. Fr´echet, Sur quelques points du calcul fonctionnel, Rendic. Circ. Mat. Palermo 22 (1906) 1–74.
[3] P. Hitzler, Generalized metrics topology in logic programming semantics, Ph. D. Thesis, National University of
Ireland (University College Cork), 2001.
[4] P. Hitzler and A. K. Seda, Dislocated topologies, J. Electr. Engin. 51 (12) (2000) 3–7.
[5] K. Menger, Probabilistic theories of relations, Proc. Nat. Acad. Sci. USA. 37(3) (1951) 178–180.
[6] P. Waszkiewicz, Quantitative Continuous Domains, Ph.D. Thesis (School of Computer Science, The University
of Birmingham, Edgbaston, Birmingham, 2002.
[7] P. Waszkiewicz, The local triangle axioms in topology and domain theory, Appl. General Top. 4 (1) (2003) 47–70.
[8] E. Zeidler, Nonlinear Functional Analysis and its Applications, I: Fixed Point Theorems, Springer-Verlag, New
York Inc. (1986).
[9] M. A. Ahmed, F.M. Zeyada and G.F. Hassan, Fixed point theorems in generalized types of dislocated metric spaces
and its applications, Thai J. Math. 11(1) (2013) 67–73
Volume 13, Issue 1
March 2022
Pages 831-836
  • Receive Date: 27 October 2019
  • Revise Date: 20 December 2019
  • Accept Date: 26 December 2019