Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

6 Issues per year


IMPACT FACTOR 2017: 0.314
5-year IMPACT FACTOR: 0.462

CiteScore 2017: 0.46

SCImago Journal Rank (SJR) 2017: 0.339
Source Normalized Impact per Paper (SNIP) 2017: 0.845

Mathematical Citation Quotient (MCQ) 2017: 0.26

Online
ISSN
1337-2211
See all formats and pricing
More options …
Volume 68, Issue 5

Issues

A note on a Banach’s fixed point theorem in b-rectangular metric space and b-metric space

Zoran D. Mitrović
  • Nonlinear Analysis Research Group Ton Duc Thang University Ho Chi Minh City Vietnam
  • Faculty of Mathematics and Statistics Ton Duc Thang University Ho Chi Minh City Vietnam
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2018-10-20 | DOI: https://doi.org/10.1515/ms-2017-0172

Abstract

In this note we give very short proofs for Banach contraction principle theorem in the b-rectangular metric spaces and b-metric spaces. Our result provides a complete solution to an open problem raised by George, Radenović, Reshma and Shukla.

MSC 2010: Primary 47H10

Keywords: fixed points; b-metric space; rectangular metric space; b-rectangular metric space

References

  • [1]

    BAKHTIN, I. A.: The contraction mapping principle in quasimetric spaces, Funct. Anal., Unianowsk Gos. Ped. Inst. 30 (1989), 26–37.Google Scholar

  • [2]

    BUDHIA, L.—KIR, M.—GOPAL, D.—KIZILTUNÇ, H.: New fixed point results in rectangular metric space and application to fractional calculus, Tbil. Math. J. 10 (2017), 91–104.Google Scholar

  • [3]

    CZERWIK, S.: Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav. 1 (1993), 5–11.Google Scholar

  • [4]

    EGE, O.: Complex valued rectangular b-metric spaces and an application to linear equations, J. Nonlinear Sci. Appl. 8 (2015) 1014-1021Google Scholar

  • [5]

    GEORGE, R.—RADENOVIĆ, S.—RESHMA, K. P.—SHUKLA, S.: Rectangular b-metric space and contraction principles, J. Nonlinear Sci. Appl. 8 (2015) 1005-1013Google Scholar

  • [6]

    KHAMSI, M. A.: Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl. (2010), Article ID 315398, 7 pages.Google Scholar

  • [7]

    KHAMSI, M. A.—HUSSAIN, N.: KKM mappings in metric type spaces, Nonlinear Anal. 73 (2010) 3123-3129Google Scholar

  • [8]

    RAD, G. S.—RADENOVIĆ, S.—DOLIĆANIN-DJEKIĆ, D.: A shorter and simple approach to study fixed point results via b-simulation functions, Iran. J. Math. Sci. Inform., to appear.Google Scholar

About the article

Received: 2017-01-16

Accepted: 2017-03-28

Published Online: 2018-10-20

Published in Print: 2018-10-25


(Communicated by L'ubica Holá)


Citation Information: Mathematica Slovaca, Volume 68, Issue 5, Pages 1113–1116, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0172.

Export Citation

© 2018 Mathematical Institute Slovak Academy of Sciences.Get Permission

Comments (0)

Please log in or register to comment.
Log in