Hermite-Hadamard type inequalities for operator s-preinvex functions

Volume 8, Issue 6, pp 1070--1081 http://dx.doi.org/10.22436/jnsa.008.06.17

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Authors

Shu-Hong Wang - School of Mathematical Sciences, Dalian University of Technology, 116024 Dalian, China. Xi-Min Liu - School of Mathematical Sciences, Dalian University of Technology, 116024 Dalian, China. - College of Mathematics, Inner Mongolia University for the Nationalities, 028043 Tongliao, China.

Abstract

In this paper, we introduce the concept of operator s-preinvex function, establish some new Hermite- Hadamard type inequalities for operator s-preinvex functions, and provide the estimates of both sides of Hermite-Hadamard type inequality in which some operator s-preinvex functions of positive selfadjoint operators in Hilbert spaces are involved.

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Keywords

• Hermite-Hadamard type inequality
• operator s-convex function
• operator preinvex function
• operator s-preinvex function.

MSC

•  47A63
•  26D07
•  26D10
•  26D15
•  26D99

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