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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


IMPACT FACTOR 2018: 0.490

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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
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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.CrossrefWeb of ScienceGoogle 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) 1014-1021CrossrefGoogle Scholar

  • [5]

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

  • [7]

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

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