On lattice-valued maps stemming from the notion of optimal average

被引：0
作者：
N. K. Agbeko
W. Fechner
E. Rak
机构：
[1] University of Miskolc,Institute of Mathematics
[2] Łódź University of Technology,Institute of Mathematics
[3] University of Rzeszów,Faculty of Mathematics and Natural Sciences
来源：
Acta Mathematica Hungarica | 2017年 / 152卷
关键词：
functional equation; functional inequality; optimal average; lattice; semigroup; primary 39B82; secondary 06B99; 06F05; 06F20; 46A40; 20M15; 39B42; 39B52; 39B62; 39B72;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The main purpose of this paper is to study certain lattice-valued maps through associated functional equations and inequalities. We deal with morphisms between an algebraic structure and an ordered structure. Next, we solve a separation problem for the inequalities studied. Moreover, we discuss the Hyers-Ulam stability of our main equation. Our research is motivated by the notion of optimal average, which was introduced by the first author in 1994.
引用
收藏
页码：72 / 83
页数：11
相关论文
共 16 条
[1]  
Agbeko N.K.(1994)On optimal averages, Acta Math. Hungar., 63 133-147
[2]  
Agbeko N.K.(1995)On the structure of optimal measures and some of its applications, Publ. Math. Debrecen, 46 79-87
[3]  
Agbeko N.K.(2001)Mapping bijectively σ-algebras onto power sets, Miskolc Math. Notes, 2 85-92
[4]  
Agbeko N.K.(2013)The extension of some Orlicz space results to the theory of optimal measure, Math. Nachr., 286 760-771
[5]  
Dragomir S.S.(1950)On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 64-66
[6]  
Tosio Aoki(1991)On separation theorem for subadditive and superadditive functionals, Studia Math., 100 25-38
[7]  
Gajda Z.(1941)On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 27 222-224
[8]  
Kominek Z.(1966)Interpolation of additive functionals, Studia Math., 27 269-272
[9]  
Hyers D.H.(1987)On the abstract Hahn–Banach Theorem due to Rodé, Aequationes Math 34 89-95
[10]  
Kaufman R.(1972)Additive functionals on abelian semigroups, Comment. Math. Prace Mat., 16 239-246
12