Page 140 - IJOCTA-15-1

R. Bagri, G. Sachdev, D. Agarwal / IJOCTA, Vol.15, No.1, pp.123-136 (2025)

T
¯
¯ τ β ϱ (Π, ¯σ κ , ¯µ) dν ≦0. Acknowledgments
Using dual constraints (23) and (24), we obtain The authors would like to extend our gratitude to
Dr. Vishakha Jadaun for her invaluable contribu-
Z
tion which helped in enhancing the quality of the
¯
¯
¯
T
η(t, ¯σ, ζ, ¯σ κ , ζ κ , ¯ω, ¯ϱ) − ¯χ Ψ ζ (Π, ¯ a)+ paper.
Ω

¯ T ¯ ¯ T ¯
D κ λ θ ζ κ (Π, ¯σ κ , b)+ ¯τ β ζ κ (Π, ¯σ κ , ¯µ) dν
Funding
Z

¯
¯
¯
¯
¯ T
+ D κ η(t, ¯σ, ζ, ¯σ κ , ζ κ , ¯ω, ¯ϱ) λ θ ζ κ (Π, ¯σ κ , b)+
Ω None.

T ¯
¯ τ β ζ κ (Π, ¯σ κ , ¯µ) dν
Conflict of interest
Z

¯
¯
¯
T
+ ξ(t, ¯σ, ζ, ¯σ κ , ζ κ , ¯ω, ¯ϱ) − ¯χ Ψ ϱ (Π, ¯ a) dν ≦0.
Ω The authors declare that they have no conflict of
interest regarding the publication of this article.
Further, integrating by parts and using boundary
conditions
Author contributions
Z

¯
¯
¯
T
− η(t, ¯σ, ζ, ¯σ κ , ζ κ , ¯ω, ¯ϱ)¯χ Ψ ζ (Π, ¯ a)+ Conceptualization: All authors
Ω
Formal analysis: All authors
¯
¯
¯
T
ξ(t, ¯σ, ζ, ¯σ κ , ζ κ , ¯ω, ¯ϱ)¯χ Ψ ϱ (Π, ¯ a) dν ≦0, Methodology: All authors
or Writing – original draft: All authors
Z
Writing – review & editing: All authors
¯
¯
¯
T
η(t, ¯σ, ζ, ¯σ κ , ζ κ , ¯ω, ¯ϱ)¯χ Ψ ζ (Π, ¯ a)+
Ω

¯
T
¯
¯
ξ(t, ¯σ, ζ, ¯σ κ , ζ κ , ¯ω, ¯ϱ)¯χ Ψ ϱ (Π, ¯ a) dν >0.
Availability of data
R
Thus, by strict pseudo-invexity of Ω Ψ(., ¯ a)dν Not applicable.
¯
w.r.t η and ξ at (ζ, ¯ϱ),
References
Z Z

¯
T
T
¯
¯ χ Ψ(Λ, ¯ a)dν > ¯ χ Ψ(Π, ¯ a) dν
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¯
Hence, (¯σ, ¯ω)=(ζ, ¯ϱ). Delayed Repair. Annals of Operations Research,
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