Application of Ruscheweyh q-differential operator to analytic functions of reciprocal order
In: Studia Universitatis Babeş-Bolyai. Mathematica, Band 65, Heft 2, S. 199-210
ISSN: 2065-961X
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In: Studia Universitatis Babeş-Bolyai. Mathematica, Band 65, Heft 2, S. 199-210
ISSN: 2065-961X
In: Revue roumaine de chimie: Romanian journal of chemistry, Band 64, Heft 11, S. 949-963
In: Studia Universitatis Babeş-Bolyai. Mathematica, Band 65, Heft 2, S. 183-198
ISSN: 2065-961X
In: Studia Universitatis Babeş-Bolyai. Mathematica, Band 63, Heft 4, S. 419-436
ISSN: 2065-961X
In: Studia Universitatis Babeş-Bolyai. Mathematica, Band 63, Heft 4, S. 437-445
ISSN: 2065-961X
In: Studia Universitatis Babeş-Bolyai. Mathematica, Band 62, Heft 3, S. 331-340
ISSN: 2065-961X
In: Studia Universitatis Babeş-Bolyai. Mathematica, Band 63, Heft 2, S. 257-267
ISSN: 2065-961X
In: Studia Universitatis Babeş-Bolyai. Mathematica, Band 66, Heft 4, S. 613-627
ISSN: 2065-961X
We consider positivity of sum $\sum_{i=1}^np_if(x_i)$ involving convex functions of higher order. Analogous for integral $\int_a^bp(x)f(g(x))dx$ is also given. Representation of a function $f$ via the Fink identity and the Green function leads us to identities for which we obtain conditions for positivity of the mentioned sum and integral. We obtain bounds for integral remainders which occur in those identities as well as corresponding mean value theorems.