Convexity of nonlinear mappings between bounded linear operator spaces-Reference-Cited by-同舟云学术

Convexity of nonlinear mappings between bounded linear operator spaces

Published:2024 Issue:5 Volume:9 Page:10462-10477
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Bounkhel Messaoud¹,Al-Tane Ali²

Affiliation:

1. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia; Email: bounkhel@ksu.edu.sa

2. Department of Basic Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia; Email: aaltane.c@ksu.edu.sa

Abstract

<abstract><p>Motivated by the work <sup>[<xref ref-type="bibr" rid="b7">7</xref>]</sup>, in which the author studied the convexity of nonlinear mappings defined between bounded linear operator spaces, our research extends this inquiry. In this work, we continue the study of the convexity of nonlinear mappings defined between bounded linear operator spaces and we establish a characterization in terms of the second order directional derivative. We apply the main result to prove the convexity and the nonconvexity of well-known nonlinear mappings. The case of nondifferentiable mappings is also treated in the last section.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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1. Convexity of nonlinear mappings between bounded linear operator spaces;AIMS Mathematics;2023