Geodesic
Hermite–Hadamard type inequalities via new exponential type convexity and their applications
Filomat, Tome 35 (2021) no. 6, p. 1803

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DOI

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 ψ and for the products of two (s, m)–exponential type convex functions ψ and φ 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.
DOI : 10.2298/FIL2106803B
Classification : 26A51, 26A33, 26D07, 26D10, 26D15
Keywords: Convex function, (s, m)–exponential type convexity, Hermite–Hadamard inequality, Hölder inequality, power mean inequality 
Saad Ihsan Butt; Artion Kashuri; Jamshed Nasir. Hermite–Hadamard type inequalities via new exponential type convexity and their applications. Filomat, Tome 35 (2021) no. 6, p. 1803 . doi: 10.2298/FIL2106803B
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     author = {Saad Ihsan Butt and Artion Kashuri and Jamshed Nasir},
     title = {Hermite{\textendash}Hadamard type inequalities via new exponential type convexity and their applications},
     journal = {Filomat},
     pages = {1803 },
     year = {2021},
     volume = {35},
     number = {6},
     doi = {10.2298/FIL2106803B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2106803B/}
}
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