Article ID: MTJPAM-D-22-00027

Title: On Some Pexider Type Sum Form Functional Equations

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-22-00027; Volume 4 / Issue 3 / Year 2022 (Special Issue), Pages 270-281

Document Type: Research Paper

Author(s): Dhiraj Kumar Singh a , Shveta Grover b , Surbhi Madan c

aDepartment of Mathematics, Zakir Husain Delhi College (University of Delhi), Jawaharlal Nehru Marg, Delhi 110002, India

bDepartment of Mathematics, University of Delhi, Delhi 110007, India

cDepartment of Mathematics, Shivaji College (University of Delhi), Raja Garden, Ring Road, New Delhi-110027, India

Received: 22 August 2022, Accepted: 21 December 2022, Published: 4 February 2023.

Corresponding Author: Dhiraj Kumar Singh (Email address: dhiraj426@rediffmail.com; dksingh@zh.du.ac.in)

Full Text: PDF

Abstract

Since its genesis, an equation of Pexider type has captivated the attention of the mathematical fraternity around the world. Over the decades, several Pexiderized forms of various functional equations have been studied meticulously. In comparison to the functional equations, such forms are less analysed for sum form functional equations and require substantial study. Taking lead from it, this paper is devoted to obtain the general solution of some Pexiderized forms of a sum form functional equation

$\sum\limits\limits^n_{i=1}\sum\limits\limits^m_{j=1}T\left(p_iq_j\right)\!\!=\!\sum\limits\limits^n_{i=1}T\left(p_i\right)\! \sum\limits\limits^m_{j=1}T\left(q_j\right)\!+\!\!(m\!-\!n)T(0)\sum\limits\limits^m_{j=1}T\left(q_j\right)\!+\!m(n\!-\!1)T(0),$

where T is a real-valued mapping with the domain I = [0, 1]; (p1, …, pn)∈Γn, (q1, …, qm)∈Γm and n ≥ 3, m ≥ 3 are fixed integers.

Keywords: Pexider’s equation, Sum form functional equation, Additive mapping, Multiplicative mapping, Entropy

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