Hyers - Ulam - Rassias Stability of Various Functional Equations in Non-Archimedean Neutrosophic Normed Spaces
R. Muthuraj1, K. Nachammal2, M. Jeyaraman 3,*
1 Department of Mathematics, H.H. The Rajah’s College, Pudukkottati, Affiliated to Bharathidasan University, Tiruchirappalli, Tamilnadu, India
2 Department of Mathematics, H.H. The Rajah’s College, Pudukkottati, Affiliated to Bharathidasan University, Tiruchirappalli, Tamilnadu, India
3 Department of Mathematics, Raja Doraisingam Govt. Arts College, Sivagangai, Affiliated to Alagappa University, Karaikudi, Tamilnadu, India.
Emails: rmr1973@yahoo.co.in; nachammal1976@gmail.com; jeya.math@gmail.com
Abstract
In this paper, we introduce the notion of non- Archimedean neutrosophic normed space and also establish Hyers-Ulam-Rassias-type stability results concerning the Cauchy, Pexiderized Cauchy. We determine some stability results concerning the Cauchy, Jensen and its Pexiderized functional equations in the framework of non-Archimedean Neutrosophic Normed Space. This work indeed presents a relationship between four various disciplines, the theory of neutrosophic normed space, non – Archimedean, Hyers-Ulam-Rassias stability and functional equation.
Keywords: Non-Archimedean; Pexiderized Cauchy; Functional Equation; Pexiderized Jensen Functional Equation; Neutrosophic Normed Space.