SciELO - Scientific Electronic Library Online

vol.38 número4On graded 2-classical prime submodules of graded modules over graded commutative ringsOn rough convergence of triple sequence spaces of Bernstein-Stancu operators of fuzzy numbers defined by a metric function índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados




Links relacionados

  • En proceso de indezaciónCitado por Google
  • No hay articulos similaresSimilares en SciELO
  • En proceso de indezaciónSimilares en Google


Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.4 Antofagasta dic. 2019 


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

Nehjamang Haokip1

Nilakshi Goswami2 

1Gauhati University, Dept. of Mathematics, Guwahati, AS, India, e-mail:

2Gauhati University, Dept. of Mathematics, Guwahati, AS, India, e-mail:


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.

Keywords: b-metric space; Subadditive altering distance function; Kannan type mappings.

Texto completo disponible sólo en PDF.

Full text available only in PDF format.


The authors are grateful to the referee for his valuable comments.


[1] 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: ]

[2] 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. [ Links ]

[3] 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: ]

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

[5] 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: ]

[6] 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: ]

[7] 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: ]

[8] 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: ]

[9] 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: ]

[10] 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: ]

[11] 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 [ Links ]

[12] 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. [ Links ]

[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. [ Links ]

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

[15] 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 [ Links ]

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

[17] 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. [ Links ]

[18] 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. [ Links ]

[19] 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. [ Links ]

[20] 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: ]

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

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

[23] 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. [ Links ]

[24] 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. [ Links ]

[25] 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: ]

[26] 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. [ Links ]

[27] 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, vol.2013, Article ID 159, 2013, doi: 10.1186/1687-1812-2013-159. [ Links ]

[28] 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. [ Links ]

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

[30] 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. [ Links ]

[31] 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. [ Links ]

Received: July 2018; Accepted: August 2018

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License