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Some characterizations of exponentially harmonic convex functions. (English) Zbl 1451.26017

Summary: In this paper, we define and introduce some new concepts of the exponentially harmonic convex functions. We investigate several properties of the exponentially harmonic convex functions and discuss their relations with convex functions. Optimality conditions are characterized by a class of variational inequalities, called exponentially harmonic variational inequalities. Several interesting results characterizing the exponentially convex functions are obtained. Results obtained in this paper can be viewed as significant improvement of previously known results.

MSC:

26B25 Convexity of real functions of several variables, generalizations
49J40 Variational inequalities
90C30 Nonlinear programming
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