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This research paper focuses on investigating the solvability of a constrained problem involving a nonlinear delay functional equation subject to a quadratic functional integral constraint, in two significant cases: firstly, the existence of nondecreasing
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On approximation of approximately generalized quadratic functional equation via Lipschitz criteria
Quaestiones Mathematicae. Journal of the South African Mathematical Society, 2018Let G be an Abelian group with a metric d and E ba a normed space. For any f : G → E we define the generalized quadratic difference of the function f by the formula Qk f (x, y) := f (x + ky) + f (x − ky) − f (x + y) − f (x − y) − 2(k2 − 1)f (y) for all x,
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The quadratic function and quadratic equations
1985The function f(x), where f(x) = ax2 + bx + c, and a, b, c are constants, a ≠ 0, is called a quadratic function, or sometimes a quadratic polynomial. From elementary algebra $${(x + d)^2} \equiv {x^2} + 2dx + {d^2}.$$ Using this, we write $$a{x^2} + bx + c \equiv a\left( {{x^2} + \frac{b}{a}x + \frac{c}{a}} \right) \equiv a\left[ {{{\left( {x
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