Generalized Nonsmooth Exponential-Type Vector Variational-Like Inequalities and Nonsmooth Vector Optimization Problems in Asplund Spaces

Syed Shakaib Irfan, Mijanur Rahaman, Iqbal Ahmad, Rais Ahmad and Saddam Husain
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Syed Shakaib Irfan: College of Engineering, Qassim University, Buraidah 51452, Al-Qassim, Saudi Arabia
Mijanur Rahaman: Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
Iqbal Ahmad: College of Engineering, Qassim University, Buraidah 51452, Al-Qassim, Saudi Arabia
Rais Ahmad: Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
Saddam Husain: Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India

Mathematics, 2019, vol. 7, issue 4, 1-11

Abstract: The aim of this article is to study new types of generalized nonsmooth exponential type vector variational-like inequality problems involving Mordukhovich limiting subdifferential operator. We establish some relationships between generalized nonsmooth exponential type vector variational-like inequality problems and vector optimization problems under some invexity assumptions. The celebrated Fan-KKM theorem is used to obtain the existence of solution of generalized nonsmooth exponential-type vector variational like inequality problems. In support of our main result, some examples are given. Our results presented in this article improve, extend, and generalize some known results offer in the literature.

Keywords: vector variational-like inequalities; vector optimization problems; limiting ( p , r )- ? -( ? , ? )-invexity; Lipschitz continuity; Fan-KKM theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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