Some remarks on contraction mappings in rectangular b-metric spaces
DOI:
https://doi.org/10.5269/bspm.41754Resumo
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.
Referências
1. I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal., Ulianowsk Gos. Ped. Inst., 30 (1989), 26-37.
2. S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav., 1 (1993), 5-11.
3. 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.
4. 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.
5. R. George, S. Radenovic, K. P. Reshma, S. Shukla, Rectangular b-metric space and contraction principles, J. Nonlinear Sci. Appl. 8 (2015), 1005-1013.
6. R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60, (1968), 71-76.
7. Z. D. Mitrovic, On an open problem in rectangular b-metric space, J. Anal., 25, No. 1, (2017), 135-137.
8. S. Reich, Some remarks concerning contraction mappings, Canad. Math. Bull., 14 (1971), 121-124.
9. 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.
2. S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav., 1 (1993), 5-11.
3. 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.
4. 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.
5. R. George, S. Radenovic, K. P. Reshma, S. Shukla, Rectangular b-metric space and contraction principles, J. Nonlinear Sci. Appl. 8 (2015), 1005-1013.
6. R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60, (1968), 71-76.
7. Z. D. Mitrovic, On an open problem in rectangular b-metric space, J. Anal., 25, No. 1, (2017), 135-137.
8. S. Reich, Some remarks concerning contraction mappings, Canad. Math. Bull., 14 (1971), 121-124.
9. 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.
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2020-10-11
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