Some remarks on contraction mappings in rectangular b-metric spaces
Resumen
In this paper, we give a short proof for Reich contraction in rectangular b-metric spaces with increased range of the Lipschtzian constants and illustrate this with a suitable example. Our results generalize, improve and complement several ones in the existing literature.
Descargas
Citas
I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal., Ulianowsk Gos. Ped. Inst., 30 (1989), 26-37.
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav., 1 (1993), 5-11.
H. S. Ding, M. Imdad, S. Radenovic, J. Vujakovic,On some fixed point results in b-metric, rectangular and b-rectangular metric spaces. Arab J. Math. Sci. 22(2), (2016), 151-164.
H. S. Ding, V. Ozturk, S. Radenovi´c,On some new fixed point results in b-rectangular metric spaces J. Nonlinear Sci. Appl., 8 (2015), 378–386.
R. George, S. Radenovic, K. P. Reshma, S. Shukla, Rectangular b-metric space and contraction principles, J. Nonlinear Sci. Appl. 8 (2015), 1005-1013.
R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60, (1968), 71-76.
Z. D. Mitrovic, On an open problem in rectangular b-metric space, J. Anal., 25, No. 1, (2017), 135-137.
S. Reich, Some remarks concerning contraction mappings, Canad. Math. Bull., 14 (1971), 121-124.
J. R. Roshan, V, Parvaneh, Z. Kadelburg, N. Hussain,New fixed point results in b-rectangular metric spaces, Nonlinear Anal., Model. Control, 21(5), (2016), 614-634.
Derechos de autor 2020 Boletim da Sociedade Paranaense de Matemática
Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
