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Strongly convex solutions of an iterative functional equation

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Abstract

Schauder’s fixed point theorem and the Banach contraction principle are used to study an iterative functional equation. We give sufficient conditions for the existence, uniqueness, and stability of the strongly convex and strongly concave solutions. We also give the approximate sequences for the corresponding solutions. Finally, some examples are considered for our results.

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Authors and Affiliations

  1. School of Mathematics, Chongqing Normal University, Chongqing, 401331, People’s Republic of China

    Hou Yu Zhao

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  1. Hou Yu Zhao
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Correspondence to Hou Yu Zhao.

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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 (Grant No. cstc2020jcyj-msxmX0857), Research Project of Chongqing Education Commission (Grant No. CXQT21014)

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Zhao, H.Y. Strongly convex solutions of an iterative functional equation. Aequat. Math. 96, 1007–1026 (2022). https://doi.org/10.1007/s00010-022-00877-3

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  • DOI: https://doi.org/10.1007/s00010-022-00877-3

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