Convexity of nonlinear mappings between bounded linear operator spaces

Messaoud Bounkhel; Ali Al-Tane; Messaoud Bounkhel; Ali Al-Tane

doi:10.3934/math.2024511

AIMS Mathematics

2024, Volume 9, Issue 5: 10462-10477. doi: 10.3934/math.2024511

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Research article

Convexity of nonlinear mappings between bounded linear operator spaces

Messaoud Bounkhel ^{1
,
,},
Ali Al-Tane ^{2
,}

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
Correction on: AIMS Mathematics 9: 15699–15700.

Received: 06 November 2023 Revised: 09 February 2024 Accepted: 23 February 2024 Published: 18 March 2024
MSC : 47B47, 47A30

Motivated by the work ^[7], 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.
- nonlinear mapping,
- directional derivative,
- second order directional derivative,
- Bounded linear operators,
- nondifferentiable convex mappings
Citation: Messaoud Bounkhel, Ali Al-Tane. Convexity of nonlinear mappings between bounded linear operator spaces[J]. AIMS Mathematics, 2024, 9(5): 10462-10477. doi: 10.3934/math.2024511

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Abstract

Motivated by the work ^[7], 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.

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