Abstract
Some uses of the convexity of a function are to find the optimal value of the function. In certain domains, the first type s-convex function is a generalization of the convex function, and studies on the optimality of the first type s-convex function are still few. What is studied in this article includes the optimality of the first type s-convex function in the complex plane. Among them, the "monotonicity" property of the first-type convex function on a ray, continuity at the origin, and justification that the first-type s-convex function in the complex plane reaches its minimum value at the origin have been obtained. In addition to the optimality problem, this article also examines the necessary and sufficient conditions for the first type s-convexity of a function in the complex plane, and the inclusion property between two different s-convex function classes. Several inequalities related to the first type s-convex function have also been obtained, including the Jensen-type inequality, the Young-type inequality, and other inequalities that hold in the complex plane but not in 2-dimensional Euclidean space. The results in this article open new perspectives in the study of convex analysis and optimization theory.
Keywords
Complex Plane, Continuous, Inclusion, Jensen's inequality, Monotone, -Convex functions, Young's inequality
Subject Area
Mathematics
Article Type
Article
First Page
3629
Last Page
3648
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
How to Cite this Article
Hazmy, Sofihara Al; Asih, Endang Cahya Mulyaning; Masta, Al Azhary; and Sumiaty, Encum
(2026)
"First Type S-Convex Function on Complex Plane,"
Baghdad Science Journal: Vol. 23:
Iss.
10, Article 16.
DOI: https://doi.org/10.21123/2411-7986.5435
