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Optimality conditions and duality results in Banach space under ρ − (η, θ)-B-invexity

Author

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  • C. Nahak

    (IIT Kharagpur)

  • N. Behera

    (KIIT University)

  • S. Nanda

    (KIIT University)

Abstract

In this paper we introduce the notion of $$\rho -(\eta , \theta )$$ ρ - ( η , θ ) -B-invex function and generalized $$\rho -(\eta ,\theta )$$ ρ - ( η , θ ) -B-invex function between Banach spaces. By considering these functions, sufficient optimality conditions are obtained for a single objective optimization problem in Banach space. Duality results (i.e. weak duality, strong duality and converse duality of Mond–Weir type and similar to Mixed type duals) are established under $$\rho -(\eta , \theta )$$ ρ - ( η , θ ) -B-invexity and weak and strong duality of Mond–Weir type dual are also established under generalized $$\rho -(\eta ,\theta )$$ ρ - ( η , θ ) -B-invexity in Banach space.

Suggested Citation

  • C. Nahak & N. Behera & S. Nanda, 2017. "Optimality conditions and duality results in Banach space under ρ − (η, θ)-B-invexity," OPSEARCH, Springer;Operational Research Society of India, vol. 54(1), pages 107-121, March.
    • Handle: RePEc:spr:opsear:v:54:y:2017:i:1:d:10.1007_s12597-016-0269-2
    DOI: 10.1007/s12597-016-0269-2
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    References listed on IDEAS

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    1. S.K. Padhan & C. Nahak, 2013. "Second- and higher-order generalised invexity and duality in mathematical programming," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 5(2), pages 170-182.
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