Research Article

Stability of k-Tribonacci Functional Equation in Non-Archimedean Space

by  Roji Lather, Manoj Kumar
journal cover
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 128 - Issue 14
Published: October 2015
Authors: Roji Lather, Manoj Kumar
10.5120/ijca2015906754
PDF

Roji Lather, Manoj Kumar . Stability of k-Tribonacci Functional Equation in Non-Archimedean Space. International Journal of Computer Applications. 128, 14 (October 2015), 27-30. DOI=10.5120/ijca2015906754

                        @article{ 10.5120/ijca2015906754,
                        author  = { Roji Lather,Manoj Kumar },
                        title   = { Stability of k-Tribonacci Functional Equation in Non-Archimedean Space },
                        journal = { International Journal of Computer Applications },
                        year    = { 2015 },
                        volume  = { 128 },
                        number  = { 14 },
                        pages   = { 27-30 },
                        doi     = { 10.5120/ijca2015906754 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }
                        %0 Journal Article
                        %D 2015
                        %A Roji Lather
                        %A Manoj Kumar
                        %T Stability of k-Tribonacci Functional Equation in Non-Archimedean Space%T 
                        %J International Journal of Computer Applications
                        %V 128
                        %N 14
                        %P 27-30
                        %R 10.5120/ijca2015906754
                        %I Foundation of Computer Science (FCS), NY, USA
Abstract

Throughout this paper, we investigate the Hyers-Ulam stability of k-Tribonacci functional equation if (k, x) = k f(k, x – 1) + f( k, x – 2) + f(k, x – 3) in the class of functions f : N × R → X where X is real non-archimeadean Banach space.

References
  • A. H. Sales, About K-Fibonacci numbers and their associated numbers; Int. J. of Math Forum, Vol. 6, no.50, (2011) 2473- 2479.
  • D. H. Hyers, On the stability if linear functional equation, Proc. Natl. Acad. Sci. USA. 27(1941) 221-224.
  • D. H. Hyers, G. Isac and Th. M Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Boston, 1998.
  • D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math., 44(1992) 125-153.
  • G. L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Math., 50 (1995) 143-190.
  • J.M. Rassias, On approximately of approximately linear mappings by linear mappings, J. Functional Anal. USA, 46 (1982) 126-130.
  • M. Bidkham and M. Hosseini, Hyers - Ulam stability of K-Fibonacci functional equation, Int. J. Nonlinear Anal. Appl., 2 (2011) 42-49.
  • M. Bidkham, M. Hosseini, C. park and M. Eshaghi Gordji, Nearly (k,s)- Fibonacci functional equations in β-normed spaces , Aequationes Math., 83 (2012) 131-141.
  • M. Eshaghi Gordji and H. Khodaei, Stability of Functional Equations,LAP LAMBERT Academic Publishing, 2010.
  • M. Eshaghi Gordji, A. Divandari, C. Park and D. Y. Shin ,Hyers-Ulam stability of a Tribonacci functional equation in 2-normed space , J. Comp. Anal. and Appl. Vol.6, No.3 (2014) 503-508.
  • M. Gordji, M. Naderi and Th. M.Rassias: Solution and Stability of Tribonacci functional equation in Non- Archinedean Banach spaces (2011)67-74.
  • M. S. Moslehian and Th. M. Rassias: Stability of functional equation in Non- Archimedean spaces, Applicable Analysis and Discrete Mathematics. 1 (2007) 325-334.
  • M. Eshaghi Gordji , M. Bavand Savad Kouchi, M.Bidkham Additive- Cubic functional equation from addive groups into Non- Archimedean Banach spaces, Faculty of Sci. and Math.5 ( 2013) 731-738.
  • P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math . Anal. Appl. 184 (1994) 431-436.
  • P. Gavruta and L. Gavruta, A new method for the generalized Hyers-Ulam-Rassias stability, Int. J. Nonlinear Anal. Appl., 1 (2010) 11-18.
  • R. Ger and P. Semrl, The stability of exponential equation, Proc. Amer. Math. Soc., 124 (1996) 779-787.
  • S. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, 2001.
  • S. Jung, Hyers-Ulam stability of Fibonacci functional equation, Bull. Iranian Math. Soc., 35 (2009) 217-227.
  • S. Jung, Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis, Springer Optimization and Its Applications, 48, Springer, New York, 2011. xiv+362pp. ISBN: 978-1-4419-9636-7.
  • S. M. Ulam, Problems in Modern Mathematics, Chapter VI, Science ed., Wiley, New York,1940.
  • T. Aoki: On the stability of linear transformation in Banach spaces, J. Math. Soc. Jpn. 2, (1950) 64-66.
  • Th. M. Rassias, On the stability ofthe linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978) 297-300.
  • Th. M. Rassias, Approximate homomorphisms, Aequationes Math., 44 (1992) 125-153.
  • Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci., 14 (1991) 431-434.
Index Terms
Computer Science
Information Sciences
No index terms available.
Keywords

Hyers-Ulam Stability Real Non-archimedean Banach Space k-Tribonacci functional equation.

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