International Journal of Engineering, Science and Mathematics Vol.7 Special Issue 4(1), April 2018, ISSN: 2320-0294 Impact Factor: 6.765 Journal Homepage: http://www.ijmra.us, Email: editorijmie@gmail.com Double- Blind Peer Reviewed Refereed Open Access International Journal - Included in the International Serial Directories Indexed & Listed at: Ulrich's Periodicals Directory ©, U.S.A., Open J-Gage as well as in Cabell’s Directories of Publishing Opportunities, U.S.A 8 International Journal of Engineering, Science and Mathematics http://www.ijmra.us, Email: editorijmie@gmail.com Stability of Pexiderized Functional Equation in Complex Banach Spaces: A Fixed-Point Approach Parbati Saha  Pratap Mondal  Abstract The study of Hyers-Ulam-Rassias stability for several functional equations has been wildly spreaded in the context of different areas of mathematics and such type stability in real Banach spaces along with its several extensions has been examined by a number of mathematicians. In this paper we prove the Hyers- Ulam-Rassias stability of a Pexiderized functional equation in complex Banach spaces under suitable conditions. Keywords: Hyers-Ulam stability; Pexider type functional equation; Complex Banach spaces; Alternative fixed-point theorem. Copyright © 2018 International Journals of Multidisciplinary Research Academy.All rights reserved. Author correspondence: Department of Mathematics, Bijoy Krishna Girls’ College, Howrah Howrah, West Bengal, India-711101 Email: pratapmondal111@gmail.com 1. Introduction The idea of stability of functional equations, in particular, about the stability of group homomorphism, was first posed by Ulam [15] and it was first partially answered by Hyers [7] for Banach spaces. Aoki [1] generalized the result of Hyers for additive mapping and it was further generalized by Rassias [14] for linear mappings by considering an unbounded Cauchy difference. A generalization of the Rassias theorem was obtained by Gavruta [6] by replacing the unbounded Cauchy difference with a general control function in the spirit of Rassias’ approach. A number of outcomes regarding the stability problems of various functional equations have been extensively investigated by a number of researchers [3, 5, 8, 9, 10, 11]. In this paper we prove the Hyers-Ulam-Rassias stability for Pexiderized functional equation ሺ ݔ+ݕሻ= ሺݔሻ − ℎሺݕሻ in complex Banach spaces by using the fixed-point method and examine a property of the solution of the above functional equation in technical terms. 2. Mathematical Background First, we describe the notion of Pexiderized additive functional equation. A mapping :  →  is said to be an additive form if ሺݔሻ= ݔfor all ,ݔ∈. If  and  are assumed to be a real vector space and a Banach space respectively then for a mapping :  → , consider a functional equation ሺ ݔ+ ݕሻ = ሺݔሻ + ሺݕሻ . . . ሺʹ.ͳሻ. which is known as the Cauchy functional equation and any solution of ሺʹ.ͳሻ is termed as an additive mapping. Particularly, if  =  = , the additive form ሺݔሻ= ݔis a solution ofሺʹ.ͳሻ.  Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah - 711103, West Bengal, India.  Department of Mathematics, Bijoy Krishna Girls’ College, Howrah, Howrah-711101, West Bengal, India.