Inequalities of hermite-hadamard type for k-bounded modulus convex complex functions
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Dragomir, Sever S 
ORCID: 0000-0003-2902-6805
(2020)
Inequalities of hermite-hadamard type for k-bounded modulus convex complex functions.
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica, 93 (2).
pp. 11-23.
ISSN 1024-7696
Abstract
Let D ⊂ C be a convex domain of complex numbers and K > 0. We say that the function f: D ⊂ C → C is called K-bounded modulus convex, for the given K > 0, if it satisfies the condition |(1 − λ) f (x) + λf (y) − f ((1 − λ) x + λy)| ≤ 1 Kλ (1 − λ) |x − y|2 2 for any x, y ∈ D and λ ∈ [0, 1] . In this paper we establish some new Hermite-Hadamard type inequalities for the complex integral on γ, a smooth path from C, and K-bounded modulus convex functions. Some examples for integrals on segments and circular paths are also given.
| Item type | Article |
| URI | https://vuir.vu.edu.au/id/eprint/42367 |
| Official URL | http://www.mathnet.ru/eng/basm529 |
| Subjects | Current > FOR (2020) Classification > 4903 Numerical and computational mathematics Current > Division/Research > College of Science and Engineering |
| Keywords | integrals on segments, circular paths, convex domain, complex numbers |
| Citations in Scopus | 0 - View on Scopus |
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