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

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Topics in Mathematical Analysis and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 94))

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Abstract

In this paper, we consider the following affine functional equation

$$\displaystyle{f(3x+y+z)+f(x+3y+z)+f(x+y+3z)+f(x)+f(y)+f(z) = 6f(x+y+z).}$$

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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    M. Mursaleen & Khursheed J. Ansari

Authors
  1. M. Mursaleen
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  2. Khursheed J. Ansari
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Correspondence to M. Mursaleen .

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Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Department of Mathematics, University of Pécs, Pécs, Hungary

    László Tóth

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Mursaleen, M., Ansari, K.J. (2014). The Stability of an Affine Type Functional Equation with the Fixed Point Alternative. In: Rassias, T., Tóth, L. (eds) Topics in Mathematical Analysis and Applications. Springer Optimization and Its Applications, vol 94. Springer, Cham. https://doi.org/10.1007/978-3-319-06554-0_24

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