Fan-Hemicontinuity for the gradient of the norm in Hilbert space
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Marcel Bogdan
Abstract
It was claimed in [Sadeqi, I.—Salehi Paydar, M.: A comparative study of Ky Fan hemicontinuity and Brezis pseudomonotonicity of mappings and existence results, J. Optim. Theory Appl. 165(2) (2015), 344–358] that the gradient of a convex Gâteaux differentiable function is Fanhemicontinuous. The aim of the present paper is to correct this implication by exemplifying for
Acknowledgement
I thank with gratitude Professor Ştefan Cobzaş for his remarks and suggestions made during the preparation of this paper. The author thanks the reviewers for their reports on the manuscript.
(Communicated by Marek Balcerzak)
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© 2022 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Prof. RNDr. Július korbaš, CSC. passed away
- Kalmbach measurability In d0-algebras
- Quantifiers on L-algebras
- Ideals of functions with compact support in the integer-valued case
- An algebraic study of the logic S5’(BL)
- Triangular numbers and generalized fibonacci polynomial
- A general matrix series inversion pair and associated polynomials
- Quantum ostrowski type inequalities for pre-invex functions
- Hermite-Hadamard type inequalities for interval-valued fractional integrals with respect to another function
- Approximating families for lattice outer measures on unsharp quantum logics
- On a generalized Lamé-Navier system in ℝ3
- Coercive and noncoercive elliptic problems with variable exponent Laplacian under Robin boundary conditions
- On some classical properties of normed spaces via generalized vector valued almost convergence
- Fan-Hemicontinuity for the gradient of the norm in Hilbert space
- Solvability of mixed problems for heat equations with two nonlocal conditions
- The global harnack estimates for a nonlinear heat equation with potential under finsler-geometric flow
- A note on set-star-K-Menger spaces
- A bivariate extension of the Omega distribution for two-dimensional proportional data
- Bernstein polynomials based iterative method for solving fractional integral equations
- The symmetric 4-Player gambler’s problem with unequal initial stakes
- Enveloping action: Convergence spaces
Articles in the same Issue
- Prof. RNDr. Július korbaš, CSC. passed away
- Kalmbach measurability In d0-algebras
- Quantifiers on L-algebras
- Ideals of functions with compact support in the integer-valued case
- An algebraic study of the logic S5’(BL)
- Triangular numbers and generalized fibonacci polynomial
- A general matrix series inversion pair and associated polynomials
- Quantum ostrowski type inequalities for pre-invex functions
- Hermite-Hadamard type inequalities for interval-valued fractional integrals with respect to another function
- Approximating families for lattice outer measures on unsharp quantum logics
- On a generalized Lamé-Navier system in ℝ3
- Coercive and noncoercive elliptic problems with variable exponent Laplacian under Robin boundary conditions
- On some classical properties of normed spaces via generalized vector valued almost convergence
- Fan-Hemicontinuity for the gradient of the norm in Hilbert space
- Solvability of mixed problems for heat equations with two nonlocal conditions
- The global harnack estimates for a nonlinear heat equation with potential under finsler-geometric flow
- A note on set-star-K-Menger spaces
- A bivariate extension of the Omega distribution for two-dimensional proportional data
- Bernstein polynomials based iterative method for solving fractional integral equations
- The symmetric 4-Player gambler’s problem with unequal initial stakes
- Enveloping action: Convergence spaces