| Summary: | As a generalization of a geodesic function, this paper introduces the notion of the geodesic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>φ</mi><mi>E</mi></msub></semantics></math></inline-formula>-convex function. Some properties of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>φ</mi><mi>E</mi></msub></semantics></math></inline-formula>-convex function and geodesic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>φ</mi><mi>E</mi></msub></semantics></math></inline-formula>-convex function are established. The concepts of a geodesic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>φ</mi><mi>E</mi></msub></semantics></math></inline-formula>-convex set and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>φ</mi><mi>E</mi></msub></semantics></math></inline-formula>-epigraph are also given. The characterization of geodesic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>φ</mi><mi>E</mi></msub></semantics></math></inline-formula>-convex functions in terms of their <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>φ</mi><mi>E</mi></msub></semantics></math></inline-formula>-epigraphs, are also obtained.
|
|---|