# Application of fixed point theory for approximating of a positive-additive functional equation in intuitionistic random C*-algebras

Volume 10, Issue 5, pp 2402--2407 Publication Date: May 25, 2017
• 407 Views

### Authors

Javad Vahidi - Department of Mathematics, Iran University of Science and Technology, Tehran, Iran.

### Abstract

We apply a fixed point theorem for approximating of a positive-additive functional equation in intuitionistic random $C^*$- algebras.

### Keywords

• Approximation
• fixed point theory
• intuitionistic
• random normed spaces
• $C^*$- algebra.

### References

• [1] A. A. N. Abdou, Y. J. Cho, R. Saadati, Distribution and survival functions with applications in intuitionistic random Lie $C^*$-algebras, J. Comput. Anal. Appl., 21 (2016), 345–354.

• [2] L. Cădariu, V. Radu, On the stability of the Cauchy functional equation: a fixed point approach, Grazer Math. Ber., 346 (2004), 43–52.

• [3] L. Cădariu, V. Radu, Fixed point methods for the generalized stability of functional equations in a single variable, Fixed Point Theory and Appl., 2008 (2008), 15 pages.

• [4] Y. J. Cho, Th. M. Rassias, R. Saadati, Stability of functional equations in random normed spaces, Springer Optimization and Its Applications, Springer, New York (2013)

• [5] Y. J. Cho, R. Saadati, Lattictic non-Archimedean random stability of ACQ functional equation, Adv. Difference Equ., 2011 (2011), 12 pages.

• [6] J. Diaz, B. Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc., 74 (1968), 305–309.

• [7] J. Dixmier, $C^*$-Algebras, North-Holland Publ. Com., Amsterdam, New York and Oxford (1977)

• [8] K. R. Goodearl, Notes on Real and Complex $C^*$-Algebras, Shiva Math. Series IV, Shiva Publ. Limited, England (1982)

• [9] J. I. Kang, R. Saadati, Approximation of homomorphisms and derivations on non-Archimedean random Lie $C^*$-algebras via fixed point method, J. Inequal. Appl., 2012 (2012), 10 pages.

• [10] S. J. Lee, R. Saadati, On stability of functional inequalities at random lattice $\phi$-normed spaces, J. Comput. Anal. Appl., 15 (2013), 1403–1412.

• [11] D. Miheţ, V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl., 343 (2008), 567–572.

• [12] D. Miheţ, R. Saadati, On the stability of the additive Cauchy functional equation in random normed spaces, Appl. Math. Lett., 24 (2011), 2005–2009.

• [13] D. Miheţ, R. Saadati, S. M. Vaezpour, The stability of the quartic functional equation in random normed spaces, Acta Appl. Math., 110 (2010), 797–803.

• [14] M. Mohamadi, Y. J. Cho, C. Park, P. Vetro, R. Saadati, Random stability on an additive-quadratic-quartic functional equation, J. Inequal. Appl., 2010 (2010), 18 pages.

• [15] C. Park, M. Eshaghi Gordji, R. Saadati, Random homomorphisms and random derivations in random normed algebras via fixed point method, J. Inequal. Appl., 2012 (2012), 13 pages.

• [16] C. Park, H. A. Kenary, S. Og Kim, Positive-additive functional equations in $C^*$-algebras, Fixed Point Theory, 13 (2012), 613–622.

• [17] J. M. Rassias, R. Saadati, Gh. Sadeghi, J. Vahidi, On nonlinear stability in various random normed spaces, J. Inequal. Appl., 2011 (2011), 17 pages.

• [18] R. Saadati, Th. M. Rassias, Y. J. Cho, Z. H. Wang, Distribution and survival functions and application in intuitionistic random approximation, Appl. Math. Inf. Sci., 9 (2015), 2535–2540.

• [19] R. Saadati, S. M. Vaezpour, Y. J. Cho, A note to paper ”On the stability of cubic mappings and quartic mappings in random normed spaces” , J. Inequal. Appl., 2009 (2009), 6 pages.

• [20] J. Vahidi, C. Park, R. Saadati , A functional equation related to inner product spaces in non-Archimedean L-random normed spaces, J. Inequal. Appl., 2012 (2012), 16 pages.