Dislocated quasi-metric stability of a multiplicative inverse functional equation

Volume 24, Issue 2, pp 140--146 http://dx.doi.org/10.22436/jmcs.024.02.05

Publication Date: January 21, 2021 Submission Date: December 26, 2020 Revision Date: January 01, 2020 Accteptance Date: January 05, 2020

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1023 Downloads
• 2080 Views

Authors

B. V. Senthil Kumar - Department of Information Technology, University of Technology and Applied Sciences, Nizwa - 611, Oman. Khalifa Al-Shaqsi - Department of Information Technology, University of Technology and Applied Sciences, Nizwa - 611, Oman. S. Sabarinathan - Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur - 603 203, Tamil Nadu, India.

Abstract

In this study, we employ the dislocated metric space stability result of an equation with one variable function to prove different stabilities of a two variable equation involving rational function in the codomain of complete dislocated quasi-metric spaces. We also extend the stabilities by taking different upper bounds.

Share and Cite

Keywords

• Functional equation
• multiplicative inverse functional equation
• Ulam stability
• dislocated quasi-metric space

MSC

•  39B82
•  39B72

References

• [1] C. T. Aage, J. N. Salunke, The results on fixed points in dislocated and dislocated quasi-metric space, Appl. Math. Sci., 2 (2008), 2941--2948
  • View Article


• [2] C. T. Aage, J. N. Salunke, Some results of fixed point theorem in dislocated quasi-metric spaces, Bull. Marathwada Math. Soc., 9 (2008), 1--5
  • View Article


• [3] M. R. Abdollahpour, R. Aghayari, M. T. Rassias, Hyers-Ulam stability of associated Laguerre differential equations in a subclass of analytic functions, J. Math. Anal. Appl., 437 (2016), 605--612
  • View Article


• [4] M. R. Abdollahpour, M. T. Rassias, Hyers-Ulam stability of hypergeometric differential equations, Aequa. Math., 93 (2019), 691--698
  • View Article


• [5] J. Aczel, J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, Cambridge (1989)
  • View Article


• [6] A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 2012 (2012), 10 pages
  • View Article


• [7] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64--66
  • View Article


• [8] A. Bodaghi, B. V. Senthil Kumar, Estimation of inexact reciprocal-quintic and reciprocal-sextic functional equations, Mathematica, 59 (2017), 3--14
  • Google Scholar


• [9] D. G. Bourgin, Classes of transformations and bordering transformations, Bull. Amer. Math. Soc., 57 (1951), 223--237
  • View Article


• [10] J. Brzdek, On a method of proving the Hyers-Ulam stability of functional equations on restricted domains, Aust. J. Math. Anal. Appl., 6 (2009), 1--10
  • Google Scholar


• [11] P. W. Cholewa, Remarks on the stability of functional equations, Aequationes Math., 27 (1984), 76--86
  • View Article


• [12] K. Cieplinski, On Ulam stability of a functional equation, Results Math., 75 (2020), 1--11
  • View Article


• [13] S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific, New York (2002)
  • View Article


• [14] A. Ebadian, M. E. Gordji, H. Khodaei, R. Saadati, G. Sadeghi, On the stability of an m-variables functional equation in random normed spaces via fixed point method, Discrete Dyn. Nat. Soc., 2012 (2012), 13 pages
  • View Article


• [15] Z. Gajda, On the stability of additive mappings, Int. J. Math. Math. Sci., 14 (1991), 431--434
  • View Article


• [16] P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mapppings, J. Math. Anal. Appl., 184 (1994), 431--436
  • View Article


• [17] B. Hejmej, Stability of functional equations in dislocated quasi-metric spaces, Ann. Math. Sil., 32 (2018), 215--225
  • View Article


• [18] H. Dutta, B. V. Senthil Kumar, Classical stabilities of an inverse fourth power functional equation, J. Interdisciplinary Math., 22 (2019), 1061--1070
  • View Article


• [19] P. Hitzler, Generalized metrics and topology in logic programming semantics, Ph.D. Thesis, School of Mathematics, Applied Mathematics and Statistics, National University Ireland, University College Cork (2001)
  • Google Scholar


• [20] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 27 (1941), 222--224
  • View Article


• [21] D. H. Hyers, G. Isac, T. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Boston (1998)
  • View Article


• [22] D. H. Hyers, T. M. Rassias, Approximate homomorphisms, Aequationes Math., 44 (1992), 125--153
  • View Article


• [23] M. Janfada, G. Sadeghi, Generalized Hyers-Ulam stability of a quadartic functional equation with involution in quasi-βnormed spaces, J. Appl. Math. Informatics, 29 (2011), 1421--1433
  • View Article


• [24] S.-M. Jung, Hyers-Ulam-Rassias stability of Functional Equations in Nonlinear Analysis, Springer, New York (2011)
  • View Article


• [25] S.-M. Jung, D. Popa, M. T. Rassias, On the stability of the linear functional equation in a single variable on complete metric groups, J. Global Optim., 59 (2014), 165--171
  • View Article


• [26] S.-M. Jung, M. T. Rassias, A linear functional equation of third order associated to the Fibonacci numbers, Abstr. Appl. Anal., 2014 (2014), 7 pages
  • View Article


• [27] S.-M. Jung, M. T. Rassias, C. Mortici, On a functional equation of trigonometric type, Appl. Math. Comput., 252 (2015), 294--303
  • View Article


• [28] P. Kannappan, Functional Equations and Inequalities with Applications, Springer, New York (2009)
  • View Article


• [29] ] G. H. Kim, Y.-H. Lee, , , 53 (2020), 1–7. 1, Stability of an additive-quadratic-quartic functional equation, Demonstr. Math., 53 (2020), 1--7
  • View Article


• [30] S. O. Kim, B. V. Senthil Kumar, A. Bodaghi, Approximation on the reciprocal-cubic and reciprocal-quartic functional equations in non-Archimedean fields, Adv. Difference Equ., 2017 (2017), 12 pages
  • View Article


• [31] Y.-H. Lee, On the Hyers-Ulam-Rassias stability of a general quintic functional equation and a general sextic functional equation, Mathematics, 7 (2019), 1--14
  • View Article


• [32] Y.-H. Lee, S.-M. Jung, M. T. Rassias, On an n-dimensional mixed type additive and quadratic functional equation, Appl. Math. Comput., 228 (2014), 13--16
  • View Article


• [33] Y.-H. Lee, S.-M. Jung, M. T. Rassias, Uniqueness theorems on functional inequalities concerning cubic-quadratic-additive equation, J. Math. Inequal., 12 (2018), 43--61
  • View Article


• [34] C. Mortici, M. T. Rassias, S.-M. Jung, On the stability of a functional equation associated with the Fibonacci numbers, Abstr. Appl. Anal., 2014 (2014), 6 pages
  • View Article


• [35] N. B. Okelo, Properties of complete metric spaces and their applications to computer security, information and communication technology, Evolving Trends Eng. Technol., 1 (2014), 23--28
  • View Article


• [36] C. Park, M. T. Rassias, Additive functional equations and partial multipliers in $C^∗$ -algebras, Rev. R. Acad. Cienc. Exactas Fıs. Nat. Ser. A Mat. RACSAM, 113 (2019), 2261--2275
  • View Article


• [37] M. U. Rahman, M. Sarwar, Some new fixed point theorems in dislocated quasi-metric spaces, Palest. J. Math., 5 (2016), 171--176
  • View Article


• [38] J. M. Rassias, On approximately of approximately linear mappings by linear mappings, J. Funct. Anal., 46 (1982), 126--130
  • View Article


• [39] J. M. Rassias, E. Thandapani, K. Ravi, B. V. Senthil Kumar, Functional Equations and Inequalities: Solutions and Stability Results, Word Scientific Publishing Company, Singapore (2017)
  • View Article


• [40] T. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297--300
  • View Article


• [41] T. M. Rassias, Functional Equations and Inequalities, Kluwer Academic Publishers, New York (2000)
  • View Article


• [42] K. Ravi, J. M. Rassias, B. V. Senthil Kumar, Ulam stability of generalized reciprocal functional equation in several variables, Int. J. Appl. Math. Stat., 19 (2010), 1--19
  • Google Scholar


• [43] K. Ravi, B. V. Senthil Kumar, Ulam-Gavruta-Rassias stability of Rassias reciprocal functional equation, Global J. Appl. Math. Sci., 3 (2010), 57--79
  • Google Scholar


• [44] K. Ravi, B. V. Senthil Kumar, Stability and geometrical interpretation of reciprocal type functional equation, Asian J. Curr. Eng. Maths, 1 (2012), 300--304
  • View Article


• [45] R. Saadati, G. Sadeghi, T. M. Rassias, Approximate generalized additive mappings in proper multi-CQ∗ -algebras, Filomat, 28 (2014), 677--694
  • View Article


• [46] G. Sadeghi, A fixed point approach to stability of functional equations in modular spaces, Bull. Malays. Math. Sci. Soc., 37 (2014), 333--344
  • View Article


• [47] G. Sadeghi, M. Nazarianpoor, J. M. Rassias, Solution and stability of quattuorvigintic functional equation in intuitionistic fuzzy normed spaces, Iran. J. Fuzzy Syst., 15 (2018), 13--30
  • View Article


• [48] P. K. Sahoo, P. Kannappan, Introduction to Functional Equations, CRC Press, New York (2011)
  • View Article


• [49] M. Sarwar, M. U. Rahman, G. Ali, Some fixed point results in dislocated quasi-metric (dq-metric) spaces, J. Inequal. Appl.J. Inequal. Appl., 2014 (2014), 11 pages
  • View Article


• [50] B. V. Senthil Kumar, H. Dutta, Fuzzy stability of a rational functional equation and its relevance to system design, Int. J. Gen. Syst., 48 (2019), 157--169
  • View Article


• [51] B. V. Senthil Kumar, H. Dutta, Approximation of multiplicative inverse undecic and duodecic functional equations, Math. Methods Appl. Sci., 42 (2019), 1073--1081
  • View Article


• [52] B. V. Senthil Kumar, H. Dutta, S. Sabarinathan, Approximation of a system of rational functional equations of three variables, Int. J. Appl. Comput. Math., 5 (2019), 1--16
  • View Article


• [53] B. V. Senthil Kumar, H. Dutta, Khalifa Al-Shaqsi, On a functional equation arising from subcontrary mean and its pertinences, Advances in Intelligent Systems and Computing, 4th International Conference on Computational Mathematics and Engineering Sciences, 2020 (2020), 241--247
  • View Article


• [54] B. V. Senthil Kumar, K. Al-Shaqsi, H. Dutta, Classical stabilities of multiplicative invese difference and adjoint functional equations, Adv. Difference Equ., 2020 (2020), 9 pages
  • View Article


• [55] B. V. Senthil Kumar, H. Dutta, S. Sabarinathan, Fuzzy approximations of a multiplicative inverse cubic functional equation, Soft Comput, 24 (2020), 13285--13292
  • View Article


• [56] S. M. Ulam, Problems in Modern Mathematics, Science Editions John Wiley & Sons, New York (1964)
  • View Article


• [57] J. Wang, Some further generalization of the Hyers-Ulam-Rassias stability of functional equations, J. Math. Anal. Appl, 263 (2001), 406--423
  • View Article