Open AccessFractional trapezium type inequalities for twice differentiable preinvex functions and their applications
Author(s) -
Artion Kashuri,
Rozana Liko
Publication year - 2020
Publication title -
an international journal of optimization and control: theories and applications/e-an international journal of optimization and control: theories and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.287
H-Index - 6
eISSN - 2146-5703
pISSN - 2146-0957
DOI - 10.11121/ijocta.01.2020.00795
Subject(s) - differentiable function , mathematics , type (biology) , inequality , operator (biology) , identity (music) , function (biology) , pure mathematics , computation , calculus (dental) , algebra over a field , mathematical analysis , algorithm , physics , medicine , ecology , biochemistry , chemistry , dentistry , repressor , evolutionary biology , gene , transcription factor , acoustics , biology
Trapezoidal inequalities for functions of divers natures are useful in numerical computations. The authors have proved an identity for a generalized integral operator via twice differentiable preinvex function. By applying the established identity, the generalized trapezoidal type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identified. Some applications of presented results to special means have been analyzed. The ideas and techniques of this paper may stimulate further research.