Abstract
In this present work, we obtain the solution of the generalized additive functional equation and also establish Hyers–Ulam stability results by using alternative fixed point for a generalized additive functional equation χ ∑ g = 1 l v g = ∑ 1 ≤ g < h < i ≤ l χ v g + v h + v i − ∑ 1 ≤ g < h ≤ l χ v g + v h − l 2 − 5 l + 2 / 2 ∑ g = 1 l χ v g − χ − v g / 2 . where l is a nonnegative integer with ℕ − 0,1,2,3,4 in Banach spaces.
Highlights
Introduction e problem of UlamHyers stability concerns determining circumstances under which, given an approximate solution of a functional equation, one may locate an exact key that is closer to it in some sense. e investigation of stability problem for functional equations is identified to a question of Ulam [1] about the stability of group homomorphisms and affirmatively answered for Banach space by Hyers [2, 3]
Rassias investigated the Hyers–Ulam stability results for the various functional equations in [7–10] through different spaces
Czerwik [11, 12] examined the stability of the quadratic functional equation involving several variables in the normed spaces
Summary
Introduction e problem of UlamHyers stability concerns determining circumstances under which, given an approximate solution of a functional equation, one may locate an exact key that is closer to it in some sense. e investigation of stability problem for functional equations is identified to a question of Ulam [1] about the stability of group homomorphisms and affirmatively answered for Banach space by Hyers [2, 3]. Numerous authors used the fixed-point method to investigate several functional equations [36–41]. We derive the solution of the generalized additive functional equation along with established Hyers–Ulam stability results by using direct and fixed-point methods for a generalized additive functional equation Journal of Mathematics l χ⎛⎝ vg⎞⎠ χvg + vh + vi −
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