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IPM
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“School of Mathematics”

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Paper   IPM / M / 11332
School of Mathematics
  Title:   Application of a new integral expansion for solving a class of functional equations
  Author(s):  M. Masjed-Jamei (Joint with H. M. Srivastava)
  Status:   Published
  Journal: Appl. Math. Lett.
  Vol.:  23
  Year:  2010
  Pages:   421-425
  Supported by:  IPM
  Abstract:
In a recent paper [M. Masjed-Jamei, H.M. Srivastava, An integral expansion for analytic functions based upon the remainder values of the Taylor series expansions, Appl. Math. Lett. 22 (2009) 406?411], a new type of integral expansions for analytic functions was introduced and investigated. In this sequel to our earlier paper, we make use of the aforementioned expansion in order to explicitly obtain the general solutions of the following functional equation:

f(k+1)(a)+bkfk(a)=ck

(k ∈ \mathbbN0:=\mathbbN∪{0}; \mathbbN:={1,2,3,...})
for various kinds of real sequences {bk} and {ck}, where (as usual) f(k)(a) is the kth derivative of the unknown function f(x) at x=a. We also present some illustrative examples in this sense.


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