In this paper, we introduce and study a new class of generalized functions, called
generalized geometrically convex functions. We establish several basic inequalities
related to generalized geometrically convex functions. We also derive several new
inequalities of the Hermite-Hadamard type for generalized geometrically convex
functions. Several special cases are discussed, which can be deduced from our main
results.

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• Generalized geometrically convex functions and inequalities