γ-Strongly convex functions and γ-subdifferentiability with application to nonlinear partial differential equations
Ikram Daidai, Tijani Amahroq, Aicha Syam · European Journal of Mathematics and Applications · 2021
This paper introduces a new class of convex functions called γ-strongly convex functions and studies some properties of it.It also defines a new subdifferentiability called γ-subdifferentiability and investigate some properties of it.A characterization of lower semicontinuous γ-strongly convex functions in Banach spaces is shown.Then we remove to present a result concerning optimization problems for γ-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.