Open AccessHermite-Hadamard type inequalities via new exponential type convexity and their applications
Author(s) -
Saad Butt Ihsan,
Artion Kashuri,
Jamshed Nasir
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2106803b
Subject(s) - mathematics , exponential type , hermite polynomials , convex function , exponential function , midpoint , convexity , type (biology) , hadamard transform , jensen's inequality , pure mathematics , regular polygon , mathematical analysis , algebraic number , convex analysis , convex optimization , geometry , ecology , financial economics , economics , biology
In this paper, authors study the concept of (s,m)-exponential type convex functions and their algebraic properties. New generalizations of Hermite-Hadamard type inequality for the (s,m)-exponential type convex function ? and for the products of two (s,m)-exponential type convex functions ? and ? are proved. Some refinements of the (H-H) inequality for functions whose first derivative in absolute value at certain power are (s,m)-exponential type convex are obtain. Finally, many new bounds for special means and new error estimates for the trapezoidal and midpoint formula are provided as well.