Functional Inequalities and Equations

Dear Colleagues,

The most powerful methods for solving functional equations are direct and fixed point methods. These methods originated from the Hyers-Ulam method, which was created by the prominent mathematicians Hyers and Ulam. Their theory and method have continuously been the focus of the research of many well-known mathematicians, computer scientists and physicists. Although the direct method technique is well-known, the method still attracts the attention of many researchers, and new results are published on a regular basis. This Special Issue is devoted to the recent development of the theory of functional equations and inequalities and its applications for solving physically and biologically motivated equations and models. In particular, the issue welcomes articles devoted to the analysis and classification of Banach algebras, which are invariance algebras of real world models; stability problems of nonlinear ODE and PDEs; and the application of functional inequality and equation-based methods for finding new exact solutions of nonlinear problems arising in various applications. Articles and reviews devoted to the theoretical foundations of functional equation and inequality-based methods and their applications for solving other nonlinear and nonlinear models are also welcome.

In the analysis and classification of Banach algebras, derivations and homomorphisms in Banach algebras play important roles. The construction of symmetric and anti-symmetric bi-derivations and bi-homomorphisms in Banach algebra containing C*-algebras and C*-ternary algebras are devoted to understanding the structure of Banach algebras. In the analysis, the Hyers–Ulam stability method has been proposed for finding exact solutions of nonlinear functional equation and functional inequality. Also, using the Hyers-Ulam stability method, nonlinear partial differential equations can be reduced to nonlinear ordinary differential equations, which has the advantage of almost providing a solution. By using the Hyers-Ulam stability method, i.e., the direct method and fixed point method, the exact solution of the functional equation and functional inequality can be obtained.

For this Special Issue, we would like to invite original research and review articles that (i) focus on and highlight the direct method and fixed point method in the investigation of functional equations, that (ii) center on recent developments of the theory of functional equations and functional inequality and its applications for solving physically and biologically motivated equations and models, or that (iii) concentrate on symmetric and anti-symmetric bi-derivations and bi-homomorphisms in Banach algebras or derivations and homomorphisms in Banach algebras.

Prof. Dr. Dong Yun Shin
Guest Editor

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• functional inequality
• functional equation
• Hyers-Ulam stability
• Banach algebra
• fixed point method
• direct method
• nonlinear differential equation
• C*-ternary algebra
• bi-homomorphism
• bi-derivation
• derivation
• homomorphism
• C*-algebra