Article

Introduction to potential theory in the class of m-convex functions

Azimbay SadullaevNational University of Uzbekistan, Mathematical Institut of Uzbek Akademy, Tashkent, UzbekistanРуслан ШариповUrgench State University, Mathematical Institut of Uzbek Akademy, Urgench, Uzbekistan

Filomatjournal2025en

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Abstract

In this work we will give the very initial concepts of potential theory (m-cv polar sets, m-cv measures and their properties) in the class of m-convex (m-cv) functions in the domain D ? Rnx. In particular, we will prove that for a m ? cv measure ?*(x, E,D) its Hessian Hn?m+1,?* = 0 in the domain D\E.

Topics

Analytic and geometric function theory Optimization and Variational Analysis Functional Equations Stability Results

Identifiers

DOI: 10.2298/fil2509029s

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