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

  • Zoran D. Mitrović EMAIL logo
From the journal Mathematica Slovaca

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
  1. (Communicated by L'ubica Holá)

References

[1] BAKHTIN, I. A.: The contraction mapping principle in quasimetric spaces, Funct. Anal., Unianowsk Gos. Ped. Inst. 30 (1989), 26–37.Search in 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), 91–104.10.1515/tmj-2017-0006Search in Google Scholar

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

[4] EGE, O.: Complex valued rectangular b-metric spaces and an application to linear equations, J. Nonlinear Sci. Appl. 8 (2015) 1014-102110.22436/jnsa.008.06.12Search in Google Scholar

[5] GEORGE, R.—RADENOVIĆ, S.—RESHMA, K. P.—SHUKLA, S.: Rectangular b-metric space and contraction principles, J. Nonlinear Sci. Appl. 8 (2015) 1005-101310.22436/jnsa.008.06.11Search in Google 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.10.1155/2010/315398Search in Google Scholar

[7] KHAMSI, M. A.—HUSSAIN, N.: KKM mappings in metric type spaces, Nonlinear Anal. 73 (2010) 3123-312910.1016/j.na.2010.06.084Search in Google 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.Search in Google Scholar

Received: 2017-01-16
Accepted: 2017-03-28
Published Online: 2018-10-20
Published in Print: 2018-10-25

© 2018 Mathematical Institute Slovak Academy of Sciences

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