Exponentially General Convex Functions and Variational Inequalities

Muhammad Aslam Noor (), Khalida Inayat Noor () and Michael Th. Rassias ()
Additional contact information
Muhammad Aslam Noor: University of Wah, Department of Mathematics
Khalida Inayat Noor: University of Wah, Department of Mathematics
Michael Th. Rassias: Hellenic Military Academy, Department of Mathematics and Engineering Sciences

Chapter 18 in Convex and Variational Analysis with Applications, 2026, pp 363-416 from Springer

Abstract: Abstract In this article, we define and consider some new concepts of the higher order exponentially general convex functions with respect to an arbitrary function. Some properties of the exponentially general convex functions are investigated under suitable conditions. It is shown that the optimality conditions of the higher order exponentially general convex functions are characterized by a class of variational inequalities, which is called the higher order exponentially variational inequality. Auxiliary principle technique is used to suggest some implicit method for solving exponentially general variational inequalities. Convergence analysis of the proposed method is investigated using the pseudomonotonicity of the operator. It is shown that the parallelogram laws for Banach spaces can be obtained as applications of higher order exponentially affine general convex functions. We have also discussed some properties of exponential general nonconvex variational inequalities applying the fixed point, Wiener–Hopf equations and dynamical system techniques. Some special cases also discussed. Results obtained in this paper can be viewed as refinement and improvement of previously known results.

Date: 2026
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-032-07860-5_18

Ordering information: This item can be ordered from
http://www.springer.com/9783032078605

DOI: 10.1007/978-3-032-07860-5_18

Access Statistics for this chapter

More chapters in Springer Optimization and Its Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().