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

C. Nahak (), N. Behera () and S. Nanda ()
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C. Nahak: IIT Kharagpur
N. Behera: KIIT University
S. Nanda: KIIT University

OPSEARCH, 2017, vol. 54, issue 1, No 6, 107-121

Abstract: 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.

Keywords: $$\rho -(\eta; \theta )$$ ρ - ( η; θ ) -B-invex function; Generalized $$\rho -(\eta; \theta )$$ ρ - ( η; θ ) -B-invex function; Optimality conditions; Mond–Weir type dual (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s12597-016-0269-2

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