The Stability of an Affine Type Functional Equation with the Fixed Point Alternative

M. Mursaleen () and Khursheed J. Ansari ()
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M. Mursaleen: Aligarh Muslim University
Khursheed J. Ansari: Aligarh Muslim University

A chapter in Topics in Mathematical Analysis and Applications, 2014, pp 557-571 from Springer

Abstract: Abstract In this paper, we consider the following affine functional equation f ( 3 x + y + z ) + f ( x + 3 y + z ) + f ( x + y + 3 z ) + f ( x ) + f ( y ) + f ( z ) = 6 f ( x + y + z ) . $$\displaystyle{f(3x+y+z)+f(x+3y+z)+f(x+y+3z)+f(x)+f(y)+f(z) = 6f(x+y+z).}$$ We obtain the general solution and establish some stability results by using direct method as well as the fixed point method. Further we define the stability of the above functional equation by using the fixed point alternative.

Keywords: Hyers-Ulam stability; Affine functional equation; Fixed point method; Alternative fixed point method (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-06554-0_24

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DOI: 10.1007/978-3-319-06554-0_24

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