Fractional trapezium type inequalities for twice differentiable preinvex functions and their applications

Artion Kashuri; Rozana Liko

doi:10.11121/ijocta.01.2020.00795

Authors

Artion Kashuri Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali" Vlora, ALBANIA http://orcid.org/0000-0003-0115-3079
Rozana Liko Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali" Vlora, ALBANIA http://orcid.org/0000-0003-2439-8538

DOI:

https://doi.org/10.11121/ijocta.01.2020.00795

Keywords:

Trapezium type integral inequalities, preinvexity, general fractional integrals.

Abstract

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.

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Author Biographies

Artion Kashuri, Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali" Vlora, ALBANIA

Artion Kashuri received his PhD degree from University Ismail Qemali of Vlora in 2016 in the area of Analysis. His research areas are Mathematical Inequalities, Applied Mathematics, Fractional Calculus, Quantum Calculus, etc. He has vast experience of teaching such as Differential Equations, Numerical Analysis, Calculus, Real Analysis, Complex Analysis, Topology, etc. He has more than 100 published papers in international reputation indexed journals. His current position is Lecturer in University Ismail Qemali, Department of Mathematics.

Rozana Liko, Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali" Vlora, ALBANIA

Rozana Liko received her PhD degree from University Ismail Qemali of Vlora in 2018 in the area of Applied Mathematics. Her research areas are Mathematical Inequalities, Applied Mathematics, etc. She has vast experience of teaching such as Probability and Statistics, Calculus, Linear Algebra, Real Analysis, etc. She has more than 50 published papers in international reputation indexed journals. Her current position is Lecturer in University Ismail Qemali, Department of Mathematics.

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