http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
Sabir,Masnita Misiran,Zurni Omar,Rabia Luqman 한국전산응용수학회 2023 Journal of applied mathematics & informatics Vol.41 No.5
In this paper, geometrically convex and $s$-convex functions in third and fourth sense are merged to form ($g,s$)-convex function. Characterizations of ($g,s$)-convex function, algebraic and functional properties are presented. In addition, novel functions based on the integral of ($g,s$)-convex functions in the third sense are created, and inequality relations for these functions are explored and examined under particular conditions. Further, there are also some relationships between ($g,s$)-convex function and previously defined functions. The ($g,s$)-convex function and its derivatives will then be used to extend the well-known H-H and Fejer's type inequalities. In order to obtain the previously mentioned conclusions, several special cases from previous literature for extended H-H and Fejer's inequalities are also investigated. The relation between the average (mean) values and newly created H-H and Fejer's inequalities are also examined.