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Bahyrycz, A.; Olko, J.

Stability of the equation of \((p,q)\)-Wright functions. (English) Zbl 1363.39032

Acta Math. Hung. 146, No. 1, 71-85 (2015).
For a fixed pair \((p,q)\) of real or complex numbers \(p,q\), a \((p,q)\)-Wright function \(f\) mapping a real or comlex linear space into a semigroup is defined as a solution of the functional equation \[ f(px+qy)+f(qx+py)=f(x)+f(y).{(1)} \] The authors investigate the Hyers-Ulam stability of equation (1), and they give sufficient conditions for the stability of (1) with some classes of control functions. The discussion of the optimality of the bounding constants obtained, in some particular cases, are also presented.
Reviewer: Gyula Maksa (Debrecen)

Cited in 7 Documents

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges

Keywords:

Hyers-Ulam stability; fixed point method; \((p,q)\)-Wright affine function; semigroup; functional equation
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References:

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