Turkish Journal of Analysis and Number Theory. 2023, 11(1), 19-23
DOI: 10.12691/tjant-11-1-3
Open AccessArticle
Qian Zheng1 and Shuhong Wang1,
1College of Mathematics Science, Inner Mongolia Minzu University, Tongliao, China
Pub. Date: October 15, 2023
Cite this paper:
Qian Zheng and Shuhong Wang. A Note on Quasi-p-convex Function. Turkish Journal of Analysis and Number Theory. 2023; 11(1):19-23. doi: 10.12691/tjant-11-1-3
Abstract
In this paper, we further study the quasi-p-convex function. The concepts of strictly quasi-p-convex function and quasi-p-convex cone are given and some new fundamental characterizations and operational properties of quasi-p-convex function are obtained.Keywords:
p-convex set quasi-p-convex function strictly quasi-p-convex function quasi-p-convex cone
This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit
http://creativecommons.org/licenses/by/4.0/
References:
[1] | Finetti B D. Sulle stratificazioni convesse [J]. Ann Math Pura Appl, 1949, 30(1): 173-183. |
|
[2] | Fenchel W. Convex cones, Sets and Functions [M]. Princeton: Princeton University, 1953. |
|
[3] | Yang X M. Quasi-convexity of upper semi-continuous functions [J]. Operations Research Transactions, 1999, 01: 48-51. |
|
[4] | Yang X M. Some properties of quasi-convex functions [J]. Chinese Journal of Engineering Mathematics, 1993, 01: 51-56. |
|
[5] | Yang X M. A note on criteria of quasi-convex functions [J]. Operations Research Transactions, 2001, 02: 55-56. |
|
[6] | Wang J Y, Song Y, Bai X L. E-quasiconvex functions [J]. Journal of Liaocheng University (Natural Science Edition), 2003, 03: 17-19. |
|
[7] | Lin Q W, Yu Y H. Quasi-convex functions and Hadamard’s inequality [J]. Mathematics in Practice and Theory, 2011, 41(17): 229-235. |
|
[8] | Zhang T Y, Ji A P, Qi F. Integral inequalities of Hermite-Hadamard type for harmonically quasi-convex functions [J]. Proceedings of the Jangjeon Mathematical Society, 2013, 16(3): 399-407. |
|
[9] | Bai S P. Simpson type fractional integral inequality for quasi-convex functions [J]. Journal of Inner Mongolia University for Nationalities (Natural Science Edition), 2021, 36(06): 465-470. |
|
[10] | Sevda S, Zeynep E, Gültekin T, et al. p-convex functions and some of their properties [J]. Numereical Functional Analysis and Optimization, 2021, 42(4): 443-459. |
|
[11] | Gültekin T, Zeynep E, Sevda S, et al. Quasi p-Convex Functions [J]. Applied Mathematics E-Notes, 2022, 22: 741-750. |
|
[12] | Yang X M, Rong W D. Generalized Cconvexity and Its Application [M]. Beijing: Science Press, 2017. |
|
[13] | Bayoumi A. Foundations of Complex Analysis in Non Locally Convex Spaces: Function theory Without Convexity Condition [M]. Amsterdam: North-Holland Pub. Co., 2003. |
|
[14] | Roekafellar R T. Convex Analysis [M]. Princeton: Princeton University Press, 1970. |
|