Some fixed point theorems for generalized Kannan type mappings in b-metric spaces

Authors

  • Nehjamang Haokip Gauhati University.
  • Nilakshi Goswami Gauhati University.

DOI:

https://doi.org/10.22199/issn.0717-6279-2019-04-0050

Keywords:

b-metric space, Subadditive altering distance function, Kannan type mappings

Abstract

In this paper, we prove some fixed point theorems in b-metric spaces using subadditive altering distance function. Some of these results generalize many existing fixed point theorems for Kannan type mappings. The results are justified with suitable examples.

Author Biography

Nilakshi Goswami, Gauhati University.

Dept. of Mathematics.

References

S. Agarwal, K. Qureshi and J. Nema, “A fixed point theorem for b-metric space”, International journal of pure and applied mathematical sciences, vol. 9, no. 1, pp. 45-50, 2016. [On line]. Available: https://bit.ly/2OYMcad

T. An, N. Dung and V. Hang, “General fixed point theorems on metric spaces and 2-metric spaces”, Filomat, vol. 28, no. 10, pp. 2037-2045, 2014, doi: 10.2298/FIL1410037A.

J. Baillon, R. Bruck and S. Reich, “On the asymptotic behaviour of non-expansive mappings and semi-groups in Banach spaces”, Houston journal of mathematics, 4, pp. 1-9, 1978. [On line]. Available: https://bit.ly/35QmEBU

I. Bakhtin, “The contraction mapping principle in almost metric spaces”, Funct. Anal., 30, pp. 26-37, 1989.

S. Banach, “Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales”, Fundamenta mathematicae, vol. 3, no. 1, pp. 133-181, 1922. [On line]. Available: https://bit.ly/2Br6H7t

M. Boriceanu, “Fixed point theory for multivalued generalized contraction on a set with two b-metrics”, Studia universitatis Babeș-Bolyai mathematica, vol. 54, no. 3, pp. 3-14, 2009. [On line]. Available: https://bit.ly/2J4xf2B

F. Browder and W. Peryshyn, “The solution by iteration of nonlinear functional equations in Banach spaces”, Bulletin of the american mathematical society, vol. 72, no. 3, pp. 571-575, 1966. [On line]. Available: https://bit.ly/2P1jUM9

R. Bruck and S. Reich, “Nonexpansive projections and resolvents of accretive operators in Banach spaces”, Houston journal of mathematics, vol. 3, no. 4, pp. 459-470, 1977. [On line]. Available: https://bit.ly/2P2zE1m

S. Czerwik, “Contraction mappings in b-metric spaces”, Acta mathematica et informatica universitatis ostraviensis, vol. 1, no. 1, pp. 5-11, 1993. [On line]. Available: https://bit.ly/32vRePo

D. Das and N. Goswami, “Fixed points of different contractive type mappings on tensor product spaces”, International journal of innovative research in science, engineering and technology, vol. 3, no. 7, pp. 14512-14519, 2014. [On line]. Available: https://bit.ly/35M4fX2

D. Das and N. Goswami, “Fixed points of mappings satisfying a weakly contractive type condition”, Journal of mathematical research with applications, vol. 36, no. 1, pp. 70-78, 2016, doi: 10.3770/j.issn:2095-2651.2016.01.009

D. Das and N. Goswami, “Some fixed point theorems on the sum and product of operators in tensor product spaces”, International journal of pure and applied mathematics, vol. 109, no. 3, pp. 651-663, 2016, doi: 10.12732/ijpam.v109i3.13.

D. Das, N. Goswami and V. Mishra, “Some results on fixed point theorems in Banach algebras”, International journal of analysis and applications, vol. 13, no. 1, pp. 32-40, 2017.

R. Edwards, Functional analysis: theory and applications. New York, NY: Holt, Rinehart and Winston, 1965.

H. Faraji and K. Nourouzi, “A generalization of Kannan and Chatterjea fixed point theorems in complete b-metric spaces”, Sahand communications in mathematical analysis, vol. 6, no. 1, pp. 77-86, 2017, doi: 10.22130/SCMA.2017.23831

H. Garai, T. Senapati and L. Dey, “A study on Kannan type contraction mapping”, Jul. 2017. arXiv:1707.06383v1.

J. Górnicki, “Fixed point theorems for Kannan type mappings”, Journal of fixed point theory and applications, vol. 19, no. 3, pp. 2145-2152, 2017, doi: 10.1007/s11784-017-0402-8.

N. Hussain, D. Dorić, Z. Kadelburg and S. Radenović, “Suzuki-type fixed point results in metric type spaces”, Fixed point theory and applications, vol. 2012, Article ID 126, 2012, doi: 10.1186/1687-1812-2012-126.

M. Jovanović, Z. Kadelburg, S. Radenović, “Common fixed point results in metric-type spaces”, Fixed Point Theory and Applications, vol. 2010, Article ID 978121, 2010, doi: 10.1155/2010/978121.

Z. Kadelburg, L. Paunovic and S. Radenovic, “A note on fixed point theorems for weakly T-Kannan and T -Chatterjea contractions in b-metric spaces”, Gulf journal of mathematics, vol. 3, no. 3, pp. 57-67, 2015. [On line]. Available: https://bit.ly/2oMX5kU

R. Kannan, “Some results on fixed points”, Bulletin of calcutta mathematical society, 60, pp. 71-76, 1968.

M. Khamsi, “Remarks on cone metric spaces and fixed point theorems of contractive mappings”, Fixed point theory and applications, 2010, Article ID 315398 2010, doi: 10.1155/2010/315398.

M. Kir and H. Kiziltune, “On some well known fixed point theorems in b-metric space”, Turkish journal of analysis and number theory, vol. 1, no. 1, pp. 13-16, 2013, doi: 10.12691/tjant-1-1-4.

S. Mohanta, “Coincidence points and common fixed points for expansive type mappings in b-metric spaces”, Iranian journal of mathematical sciences and informatics, vol. 11, no. 1, pp. 101-113, 2016, doi: 10.7508/ijmsi.2016.01.009.

S. Moradi, “New extensions of Kannan fixed point theorem on complete metric and generalized metric spaces”, International journal of mathematical analysis, vol. 5, no. 47, pp. 2313-2320, 2011. [On line]. Available: https://bit.ly/2MvzdLG

R. Pant and R. Panicker, “Geraghty and Ćirić type fixed point theorems in b-metric spaces”, Journal of nonlinear sciences and applications, vol. 9, no. 11, pp. 5741-5755, 2016, doi: 10.22436/jnsa.009.11.03.

J. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei and W. Shatanawi, “Common fixed points of almost generalized (ψ, ϕ)s-contractive mappings in ordered b-metric spaces”, Fixed point theory and applications, 2013, Article ID 159, 2013, doi: 10.1186/1687-1812-2013-159.

W. Sintunavarat, S. Plubtieng and P. Katchang, “Fixed point result and applications on b-metric space endowed with an arbitrary binary relation”, Fixed point theory applications, 2013, Article ID 296, 2013, doi: 10.1186/1687-1812-2013-296.

V. Subrahmanyam, “Completeness and fixed points”, Monatshefte für Mathematik, vol. 80, no. 4, pp. 325-330, 1975, doi: 10.1007/BF01472580.

B. Tripathy, S. Paul and N. Das, “A fixed point theorem in a generalized fuzzy metric space”, Boletim da Sociedade Paranaense de Matematica, vol. 32, no. 2, pp. 221-227, 2014, doi: 10.5269/bspm.v32i2.20896.

B. Tripathy, S. Paul and N. Das, “Banach’s and Kannan’s fixed point results in fuzzy 2-metric spaces”, Proyecciones (Antofagasta. En línea), vol. 32, no. 4, pp. 359-375, 2013, doi: 10.4067/S0716-09172013000400005.

Published

2019-10-21

How to Cite

[1]
N. Haokip and N. Goswami, “Some fixed point theorems for generalized Kannan type mappings in b-metric spaces”, Proyecciones (Antofagasta, On line), vol. 38, no. 4, pp. 763-782, Oct. 2019.

Issue

Section

Artículos