Open AccessNew Hadamard-type inequalities via $(s,m_{1},m_{2})$-convex functions
Author(s) -
Bahtiyar Bayraktar,
Saad Ihsan Butt,
Sh. Shaokat,
Juan E. Nápoles Valdés
Publication year - 2021
Publication title -
vestnik udmurtskogo universiteta. matematika, mehanika, kompʹûternye nauki
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.354
H-Index - 8
eISSN - 2076-5959
pISSN - 1994-9197
DOI - 10.35634/vm210405
Subject(s) - hadamard transform , convexity , mathematics , convex function , identity (music) , pure mathematics , class (philosophy) , type (biology) , operator (biology) , regular polygon , simple (philosophy) , function (biology) , mathematical analysis , computer science , physics , geometry , philosophy , repressor , artificial intelligence , ecology , chemistry , acoustics , financial economics , biology , biochemistry , epistemology , evolutionary biology , transcription factor , economics , gene
The article introduces a new concept of convexity of a function: $(s,m_{1},m_{2})$-convex functions. This class of functions combines a number of convexity types found in the literature. Some properties of $(s,m_{1},m_{2})$-convexities are established and simple examples of functions belonging to this class are given. On the basis of the proved identity, new integral inequalities of the Hadamard type are obtained in terms of the fractional integral operator. It is shown that these results give us, in particular, generalizations of a number of results available in the literature.