Strongly convex solutions of a polynomial-like iterative equation with variable coefficients

Abstract

Schauder's fixed point theorem and the Banach contraction principle are used to study the polynomial-like iterative functional equation with variable coefficients. We give sufficient conditions for the existence, uniqueness, and stability of the strongly convex and strongly concave solutions. Finally, some examples were considered by our results.

Keywords:

• Functional equation
• iteration
• strongly convex function
• fixed point

2020 Mathematics Subject Classifications:

• 39B12
• 39B82

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China (Grant No. 11971081), Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN201900525), the Natural Science Foundation of Chongqing, China (Grant No. cstc2020jcyj-msxmX0857), the Research Project of Chongqing Education Commission (Grant No. CXQT21014)