Inequalities of Hermite-Hadamard Type for K-Bounded Modulus Convex Complex Functions
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DRAGOMIR, Silvestru Sever. Inequalities of Hermite-Hadamard Type for K-Bounded Modulus Convex Complex Functions. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2020, nr. 2(93), pp. 11-23. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 2(93) / 2020 / ISSN 1024-7696 /ISSNe 2587-4322

Inequalities of Hermite-Hadamard Type for K-Bounded Modulus Convex Complex Functions

CZU: 517.5+517.98
MSC 2010: 26D15, 26D10, 30A10, 30A86.

Pag. 11-23

Dragomir Silvestru Sever
 
College of Engineering and Science Victoria University
 
 
Disponibil în IBN: 18 septembrie 2020


Rezumat

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 − ) f (x) + f (y) − f ((1 − ) x + y)| ≤ 1 2 K (1 − ) |x − y|2 for any x, y ∈ D and  ∈ [0, 1] . In this paper we establish some new HermiteHadamard type inequalities for the complex integral on , a smooth path from C, and K-bounded modulus convex functions. Some examples for integrals on segments and circular paths are also given.

Cuvinte-cheie
complex integral, Continuous functions, Holomorphic functions, Hermite-Hadamard inequality, Midpoint inequality, Trapezoid inequality

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