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

1
College of Engineering, Qassim University, Buraidah 51452, Al-Qassim, Saudi Arabia
2
Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(4), 345; https://doi.org/10.3390/math7040345
Received: 27 February 2019 / Revised: 29 March 2019 / Accepted: 4 April 2019 / Published: 10 April 2019
(This article belongs to the Special Issue Applied Functional Analysis and Its Applications)
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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. View Full-Text
Keywords: vector variational-like inequalities; vector optimization problems; limiting (p,r)-α-(η,θ)-invexity; Lipschitz continuity; Fan-KKM theorem vector variational-like inequalities; vector optimization problems; limiting (p,r)-α-(η,θ)-invexity; Lipschitz continuity; Fan-KKM theorem
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Irfan, S.S.; Rahaman, M.; Ahmad, I.; Ahmad, R.; Husain, S. Generalized Nonsmooth Exponential-Type Vector Variational-Like Inequalities and Nonsmooth Vector Optimization Problems in Asplund Spaces. Mathematics 2019, 7, 345.

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