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2016 | 31 | 48-58
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Solution and Generalized Ulam-Hyers Stability of a Reciprocal Type Functional Equation in Non-Archimedean Fields

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In this paper, we obtain the general solution of a reciprocal type functional equation of the type f(x+y)=f((k_1 x+k_2 y)/k)f((k_2 x+k_1 y)/k)/(f((k_1 x+k_2 y)/k)+f((k_2 x+k_1 y)/k) ) and investigate its generalized Ulam-Hyers stability in non-Archimedean fields where k>2, k_1 and k_2 are positive integers with k=k_1+k_2 and k_1≠k_2. We also establish Hyers-Ulam-Rassias stability, Ulam-Gavruta-Rassias stability and J.M. Rassias stability controlled by the mixed product-sum of powers of norms for the same equation.
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  • Department of Mathematics, C. Abdul Hakeem College of Engg. and Tech., Melvisharam - 632 509, Tamil Nadu, India
  • Pedagogical Department E.E., PG & Research Department of Mathematics, Sacred Heart College, Tirupattur - 635 601, Tamil Nadu, India
  • Section of Mathematics and Informatics, National and Capodistrian University of Athens, 4 Agamemnonos Str., Aghia Paraskevi, Athens, Attikis 15342, Greece
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