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On the Maximal Monotone Operators in Hadamard Spaces

Ali Moslemipour, Mehdi Roohi, Jen-Chih Yao

Abstract

In this paper, some topics of monotone operator theory in the setting of Hadamard spaces are investigated. For a fixed element $p$ in a Hadamard space $X$, the notion of $p$-Fenchel conjugate is introduced and a type of the Fenchel-Young inequality is proved. Moreover, we examine the $p$-Fitzpatrick transform and its main properties for monotone set-valued operators in Hadamard spaces. Furthermore, some relations between maximal monotone operators and certain classes of proper, convex, l.s.c. extended real-valued functions on $X\times X^{\scalebox{0.7}{$^{\lozenge}$}}$, are given.

On the Maximal Monotone Operators in Hadamard Spaces

Abstract

In this paper, some topics of monotone operator theory in the setting of Hadamard spaces are investigated. For a fixed element in a Hadamard space , the notion of -Fenchel conjugate is introduced and a type of the Fenchel-Young inequality is proved. Moreover, we examine the -Fitzpatrick transform and its main properties for monotone set-valued operators in Hadamard spaces. Furthermore, some relations between maximal monotone operators and certain classes of proper, convex, l.s.c. extended real-valued functions on ^{\lozenge}, are given.

Paper Structure

This paper contains 6 sections, 13 theorems, 73 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Flat Hadamard space
  4. $p$-Fenchel conjugate
  5. $p$-Fitzpatrick transform
  6. Conclusion

Key Result

Lemma \oldthetheorem

KakavandiAmini Let $X$ be a Hadamard space and $a,b, c, d\in X$. Then where $D$ is as in (dinnerd).

Theorems & Definitions (34)

  • Remark 1
  • Lemma \oldthetheorem
  • Definition \oldthetheorem
  • Definition \oldthetheorem
  • Definition \oldthetheorem
  • Theorem \oldthetheorem
  • Remark 2
  • Remark 3
  • Example \oldthetheorem
  • Example \oldthetheorem
  • ...and 24 more