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Volume 1 (2021), Article ID 5
This paper introduces a new class of convex functions called $\gamma$-strongly convex functions and studies some properties of it. It also defines a new subdifferentiability called $\gamma$-subdifferentiability and investigate some properties of it. A characterization of lower semicontinuous $\gamma$-strongly convex functions in Banach spaces is shown. Then we remove to present a result concerning optimization problems for $\gamma$-strongly convex functions which allows us to conclude an extension of Minty-Browder and nonlinear Lax-Milgram theorems in Banach spaces. Finally an example of nonlinear partial differential equations is provided.
How to Cite:
Ikram Daidai, Tijani Amahroq and Aicha Syam, γ-strongly convex functions and γ-subdifferentiability with application to nonlinear partial differential equations, Eur. J. Math. Appl. 1 (2021), Article ID 5. https://doi.org/10.28919/ejma.2021.1.5