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Open AccessArticle

Special Class of Second-Order Non-Differentiable Symmetric Duality Problems with (G,αf)-Pseudobonvexity Assumptions

1
Department of Mathematics, J.C. Bose University of Science and Technology, YMCA, Faridabad 121 006, India
2
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, India
3
Department of Mathematics, College of Science, King Khalid University, Abha 9004, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(8), 763; https://doi.org/10.3390/math7080763
Received: 24 June 2019 / Revised: 6 August 2019 / Accepted: 15 August 2019 / Published: 20 August 2019
(This article belongs to the Special Issue Multivariate Approximation for solving ODE and PDE)
In this paper, we introduce the various types of generalized invexities, i.e., α f -invex/ α f -pseudoinvex and ( G , α f ) -bonvex/ ( G , α f ) -pseudobonvex functions. Furthermore, we construct nontrivial numerical examples of ( G , α f ) -bonvexity/ ( G , α f ) -pseudobonvexity, which is neither α f -bonvex/ α f -pseudobonvex nor α f -invex/ α f -pseudoinvex with the same η . Further, we formulate a pair of second-order non-differentiable symmetric dual models and prove the duality relations under α f -invex/ α f -pseudoinvex and ( G , α f ) -bonvex/ ( G , α f ) -pseudobonvex assumptions. Finally, we construct a nontrivial numerical example justifying the weak duality result presented in the paper. View Full-Text
Keywords: symmetric duality; second-order; non-differentiable; (G,αf)-invexity/(G,αf)-pseudoinvexity; (G,αf)-bonvexity/(G,αf)-pseudobonvexity symmetric duality; second-order; non-differentiable; (G,αf)-invexity/(G,αf)-pseudoinvexity; (G,αf)-bonvexity/(G,αf)-pseudobonvexity
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MDPI and ACS Style

Dubey, R.; Mishra, L.N.; Ali, R. Special Class of Second-Order Non-Differentiable Symmetric Duality Problems with (G,αf)-Pseudobonvexity Assumptions. Mathematics 2019, 7, 763. https://doi.org/10.3390/math7080763

AMA Style

Dubey R, Mishra LN, Ali R. Special Class of Second-Order Non-Differentiable Symmetric Duality Problems with (G,αf)-Pseudobonvexity Assumptions. Mathematics. 2019; 7(8):763. https://doi.org/10.3390/math7080763

Chicago/Turabian Style

Dubey, Ramu; Mishra, Lakshmi Narayan; Ali, Rifaqat. 2019. "Special Class of Second-Order Non-Differentiable Symmetric Duality Problems with (G,αf)-Pseudobonvexity Assumptions" Mathematics 7, no. 8: 763. https://doi.org/10.3390/math7080763

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