INEQUALITIES OF FEJER TYPE RELATED TO GENERALIZED CONVEX FUNCTIONS WITH APPLICATIONS

被引：35

作者：

Aslani, S. Mohammadi ^{[1
]}

Delavar, M. Rostamian ^{[2
]}

Vaezpour, S. M. ^{[3
]}

机构：

[1] Islamic Azad Univ, Karaj Branch, Dept Math, Karaj, Iran

[2] Univ Bojnord, Fac Basic Sci, Dept Math, Bojnord, Iran

[3] Amirkabir Univ Technol, Dept Math, Tehran, Iran

来源：

INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS | 2018年 / 16卷 / 01期

关键词：

(eta(1); eta(2))-convex function; Fejer inequality;

D O I：

10.28924/2291-8639-16-2018-38

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with some Fejer type inequalities related to (eta(1), eta(2))-convex functions. In fact the difference between the right and middle part of Fejer inequality is estimated without using Holder's inequality when the absolute value of the derivative of considered function is (eta(1), eta(2))-convex. Furthermore we give two estimation results when the derivative of considered function is bounded and satisfies a Lipschitz condition.

引用

页码：38 / 49

页数：12

共 12 条

[1] WHAT IS INVEXITY [J].

BENISRAEL, A ;

MOND, B .

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES B-APPLIED MATHEMATICS, 1986, 28 :1-9

[2] Some generalizations of Hermite-Hadamard type inequalities [J].

Delavar, M. Rostamian ;

De La Sen, M. .

SPRINGERPLUS, 2016, 5

[3] ON η-CONVEXITY [J].

Delavar, Mohsen Rostamian ;

Dragomir, Silvestru Sever .

MATHEMATICAL INEQUALITIES & APPLICATIONS, 2017, 20 (01) :203-216

[4] Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula [J].

Dragomir, SS ;

Agarwal, RP .

APPLIED MATHEMATICS LETTERS, 1998, 11 (05) :91-95

[5]

Fejer L., 1906, MATH NATURWISS ANZ U, V24, P369

[6] ON φ-CONVEX FUNCTIONS [J].

Gordji, M. Eshaghi ;

Delavar, M. Rostamian ;

De La Sen, M. .

JOURNAL OF MATHEMATICAL INEQUALITIES, 2016, 10 (01) :173-183

[7]

Gordji ME, 2015, INT J NONLINEAR ANAL, V6, P27

[8]

Hanson M. A., 1987, Journal of Information & Optimization Sciences, V8, P201

[9]

Jeyakumar V., 1985, Methods of Operations Research, P109

[10]

Latif MA, 2015, J COMPUT ANAL APPL, V19, P725

← 1 2 →