Vol. 14, No. 3, 2021

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On some properties of the solution set of one of Wilker's inequalities for complex numbers

Aarón Guillén-Villalobos and Jorge E. Macías-Díaz

Vol. 14 (2021), No. 3, 519–530
Abstract

We state and prove properties of the solution set of the extension of one of Wilker’s inequalities to the field of complex numbers. Wilker’s inequalities are inequalities for real numbers which involve trigonometric or hyperbolic functions. We will consider one of those inequalities on the set of complex numbers, and some important analytical properties of the solution set will be proved. Some auxiliary results will be established along the way.

Keywords
Wilker-type inequalities, extension to complex numbers, analytical properties of the solution set
Mathematical Subject Classification
Primary: 30A10
Secondary: 26D05
Milestones
Received: 29 December 2020
Revised: 19 March 2021
Accepted: 29 March 2021
Published: 17 July 2021

Communicated by H. M. Srivastava
Authors
Aarón Guillén-Villalobos
Centro de Ciencias Básicas
Universidad Autónoma de Aguascalientes
Aguascalientes
Mexico
Jorge E. Macías-Díaz
Departamento de Matemáticas y Física
Universidad Autónoma de Aguascalientes
Ciudad Universitaria
Aguascalientes
Mexico
Department of Mathematics
School of Digital Technologies
Tallinn University
Tallinn
Estonia