Stability Analysis of a New Class of Series Type Additive Functional Equation in Banach Spaces: Direct and Fixed Point Techniques

P. Agilan (), K. Julietraja, Mohammed M. A. Almazah and Ammar Alsinai
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P. Agilan: Department of Mathematics, St. Joseph’s College of Engineering, OMR, Chennai 600 119, Tamil Nadu, India
K. Julietraja: Department of Mathematics, St. Joseph’s College of Engineering, OMR, Chennai 600 119, Tamil Nadu, India
Mohammed M. A. Almazah: Department of Mathematics, College of Sciences and Arts (Muhyil), King Khalid University, Muhyil 61421, Saudi Arabia
Ammar Alsinai: Department of Mathematics, University of Mysore, Manasagangotri, Mysore 570 015, Karnataka, India

Mathematics, 2023, vol. 11, issue 4, 1-19

Abstract: In this paper, the authors introduce two new classes of series type additive functional Equations (FEs). The first class of equations is derived from the sum of the squares of the alternative series and the second one is obtained from the sum of the cubes of the series. The solution of the FE is investigated using the principle of mathematical induction. The beauty of this method lies in the fact that it satisfies the property of the additive FE as well as the series. Banach spaces are one of the widely-used spaces that are very helpful to analyse the stability results of various FEs. The Banach space conditions have been applied and the stability results are established for both of the equations. Furthermore, the Banach Contraction principle and alternative of fixed point theorem are used to derive the stability results in a fixed point technique (FPT). The relationship between the FEs and both the series is established through the principle of mathematical induction in the Application section, which adds novelty to the derived results.

Keywords: additive FE; generalized Ulam–Hyers stability; Banach space; fixed point technique (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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