On a unified integral operator for φ -convex functions

Advances in Difference Equations

article

Chel Kwun, Young¹  Zahra, Moquddsa²  Farid, Ghulam³  Zainab, Saira²  Min Kang, Shin⁴ 

[1] Department of Mathematics, Dong-A University;Department of Mathematics, University of Wah;Department of Mathematics, COMSATS University Islamabad;Department of Mathematics, Gyeongsang National University

关键词: Convex function;    φ -convex function;    Integral operators;    Fractional integrals;    Conformable fractional integrals;    Bounds;   

DOI  :  10.1186/s13662-020-02761-3

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

Integral operators have a very vital role in diverse fields of science and engineering. In this paper, we use φ-convex functions for unified integral operators to obtain their upper bounds and upper and lower bounds for symmetric φ-convex functions in the form of a Hadamard inequality. Also, for φ-convex functions, we obtain bounds of different known fractional and conformable fractional integrals. The results of this paper are applicable to convex functions.

【 授权许可】

CC BY