SciELO - Scientific Electronic Library Online

vol.38 número3Oscillation of solutions to a generalized forced nonlinear conformable fractional differential equationRainbow neighbourhood number of graphs 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.3 Antofagasta ago. 2019 


Stability of two variable pexiderized quadratic functional equation in intuitionistic fuzzy Banach spaces

P. Saha1 

T. K. Samanta2

P. Mondal3 

B. S. Choudhury4

1Indian Institute Of Engineering Science and Technology, Shibpur, Department of Mathematics, Shibpur, Howrah - 711103, West Bengal, India. e-mail:

2Uluberia College, Department of Mathematics, Uluberia, Howrah, West Bengal, 711315, India. e-mail : mumpu−

3Bijoy Krishna Girls’ College, Department of Mathematics, Howrah - 711101, West Bengal, India. e-mail :

4Indian Institute Of Engineering Science and Technology, Department of Mathematics, Shibpur, Howrah - 711103, West Bengal, India. e-mail :


The present work is about the stability of a Pexiderised quadratic functional equation. The study is in the framework of intuitionistic fuzzy Banach spaces. The approach is through a fixed point method. The stability studied is Hyers-Ulam-Rassias stability type.

Keywords: Hyers-Ulam stability; Pexider type functional equation; Intuitionistic fuzzy norm; Alternative fixed point theorem

Mathematics Subject Classification (2010):  03E72; 97I70; 39B82

Texto completo disponible sólo en PDF.

Full text available only in PDF format.


The authors gratefully acknowledge the suggestions made by the learned referee.


[1] A. Grabiec, “The generalized Hyers-Ulam stability of a class of functional equations,” Publicationes Mathematicae Debrecen, vol. 48, no. 3-4, pp. 217-235, 1996. [On line]. Available: ]

[2] A. Mirmostafaee and M. Moslehian, “Fuzzy versions of Hyers-Ulam-Rassias theorem,”Fuzzy Sets and Systems, vol. 159, no. 6, pp. 720-729, Mar. 2008., doi: 10.1016/j.fss.2007.09.016. [ Links ]

[3] D. Hyers, “On the Stability of the Linear Functional Equation,” Proceedings of the National Academy of Sciences, vol. 27, no. 4, pp. 222-224, Apr. 1941, doi: 10.1073/pnas.27.4.222. [ Links ]

[4] D. Miheţ, “The fixed point method for fuzzy stability of the Jensen functional equation,” Fuzzy Sets and Systems , vol. 160, no. 11, pp. 1663-1667, Jun. 2009, doi: 10.1016/j.fss.2008.06.014. [ Links ]

[5] G. Deschrijver and E. Kerre, “On the relationship between some extensions of fuzzy set theory,” Fuzzy Sets and Systems , vol. 133, no. 2, pp. 227-235, Jan. 2003, doi: 10.1016/S0165-0114(02)00127-6. [ Links ]

[6] J. B. Diaz and B. Margolis, “A fixed point theorem of the alternative, for contractions on a generalized complete metric space,”Bulletin of the American Mathematical Society, vol. 74, no. 2, pp. 305-310, Mar. 1968, doi: 10.1090/S0002-9904-1968-11933-0. [ Links ]

[7] K. Atanassov, “Intuitionistic fuzzy sets,”Fuzzy Sets and Systems , vol. 20, no. 1, pp. 87-96, Aug. 1986, doi: 10.1016/S0165-0114(86)80034-3. [ Links ]

[8] L. Zadeh, “Fuzzy sets,”Information and Control, vol. 8, no. 3, pp. 338-353, Jun. 1965, doi: 10.1016/S0019-9958(65)90241-X. [ Links ]

[9] L. Cădariu and V. Radu, “Fixed Points and Stability for Functional Equations in Probabilistic Metric and Random Normed Spaces,”Fixed Point Theory and Applications, vol. 2009, pp. 1-19, Nov. 2009, doi: 10.1155/2009/589143. [ Links ]

[10] N. Kayal, T. Samanta, P. Saha, and B. Choudhury, “A Hyers-Ulam-Rassias stability result for functional equations in Intuitionistic Fuzzy Banach spaces,” Iranian Journal Fuzzy Systems, vol. 13, no. 5, pp. 87-96, 2016, doi: 10.22111/IJFS.2016.2755. [ Links ]

[11] P. Mondal, N. Kayal, T. Samanta, “The stability of Pexider type functional equation in intuitionistic fuzzy Banach spaces via fixed point technique,” Journal of. Hyperstructures, vol. 4, no. 1, pp. 37-49, Jun. 2015. [On line]. Available: ]

[12] P. Mondal, N. Kayal, T. Samanta, “Stability of a quadratic functional equation in intuitionistic fuzzy Banach spaces,” Journal of New Results in Science, vol. 5, no. 10, pp. 52-59, 2016. [On line]. Available: ]

[13] P. Gavruta, “A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings,”Journal of Mathematical Analysis and Applications, vol. 184, no. 3, pp. 431-436, Jun. 1994, doi: 10.1006/jmaa.1994.1211. [ Links ]

[14] P. Cholewa, “Remarks on the stability of functional equations,”Aequationes Mathematicae, vol. 27, no. 1, pp. 76-86, Mar. 1984, doi: 10.1007/BF02192660. [ Links ]

[15] R. Saadati and J. Park, “On the intuitionistic fuzzy topological spaces,”Chaos, Solitons & Fractals, vol. 27, no. 2, pp. 331-344, Jan. 2006, doi: 10.1016/j.chaos.2005.03.019. [ Links ]

[16] S. Mohiuddine and H. Şevli, “Stability of Pexiderized quadratic functional equation in intuitionistic fuzzy normed space,”Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 2137-2146, Feb. 2011, doi: 10.1016/ [ Links ]

[17] S. Czerwik, “On the stability of the quadratic mapping in normed spaces,”Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, vol. 62, no. 1, pp. 59-64, Dec. 1992, doi: 10.1007/BF02941618. [ Links ]

[18] S. Jung, “Hyers-Ulam stability of linear differential equations of first order, II,”Applied Mathematics Letters, vol. 19, no. 9, pp. 854-858, Sep. 2006, doi: 10.1016/j.aml.2005.11.004. [ Links ]

[19] S. Jung, “On the Hyers-Ulam Stability of the Functional Equations That Have the Quadratic Property,”Journal of Mathematical Analysis and Applications, vol. 222, no. 1, pp. 126-137, Jun. 1998, doi: 10.1006/jmaa.1998.5916. [ Links ]

[20] S. Jung, “Quadratic functional equations of Pexider type,”International Journal of Mathematics and Mathematical Sciences, vol. 24, no. 5, pp. 351-359, 2000, doi: 10.1155/S0161171200004075. [ Links ]

[21] S. Ulam, “Some Questions in Analysis,” inProblems in Modern Mathematics, New York: John Wiley & Sons, Inc., 1964. [ Links ]

[22] S. Shakeri, “Intuitionistic Fuzzy Stability Of Jensen Type Mapping,”Journal of Nonlinear Sciences and Applications, vol. 02, no. 02, pp. 105-112, May 2009, doi: 10.22436/jnsa.002.02.05. [ Links ]

[23] T. Aoki, “On the Stability of the linear Transformation in Banach Spaces,”Journal of the Mathematical Society of Japan, vol. 2, no. 1-2, pp. 64-66, Sep. 1950, doi: 10.2969/jmsj/00210064. [ Links ]

[24] T. Samanta, N. Kayal and P. Mondal, “The stability of a general quadratic functional equation in fuzzy Banach spaces,” Journal of Hyperstructures, vol. 1, no. 2, pp. 71-87, Dec. 2012. [On line]. Available: ]

[25] N. Kayal, P. Mondal and T. Samanta, “The generalized Hyers-Ulam-Rassias stability of a quadratic functional equation in fuzzy Banach spaces,” Journal of New Results in Science , vol. 3, no. 5, pp. 83-95, 2014, [On line]. Available: ]

[26] T. Xu, M. Rassias, W. Xu and J. Rassias, “A fixed point approach to the intuitionistic fuzzy stability of quintic and sextic functional equations,” Iranian Journal Fuzzy Systems , vol. 9, no. 5 pp. 21-40, 2012, doi: 10.22111/IJFS.2012.102. [ Links ]

[27] T. Rassias, “On the Stability of Functional Equations in Banach Spaces,”Journal of Mathematical Analysis and Applications , vol. 251, no. 1, pp. 264-284, Nov. 2000, doi: 10.1006/jmaa.2000.7046. [ Links ]

[28] V. Radu, “The fixed point alternative and the stability of functional equations,” Fixed Point Theory, vol. 4, no. 1, pp. 91-96, 2003. [On line]. Available: ]

[29] Y. Dong, “On approximate isometries and application to stability of a functional equation,”Journal of Mathematical Analysis and Applications , vol. 426, no. 1, pp. 125-137, Jun. 2015, doi: 10.1016/j.jmaa.2015.01.045. [ Links ]

[30] Z. Wang, T. Rassias, and R. Saadati, “Intuitionistic fuzzy stability of Jensen-type quadratic functional equations,”Filomat, vol. 28, no. 4, pp. 663-676, 2014, doi: 10.2298/FIL1404663W. [ Links ]

Received: March 2018; Accepted: April 2019

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