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Journals / TWMS Journal of Applied and Engineering Mathematics / 2026 / Volume: 16 Issue: 10

$\alpha$-PRE-$E$-CONVEX AND $\alpha$-$E$-CONVEX FUNCTIONS WITH APPLICATIONS TO MATHEMATICAL PROGRAMMING

Seema Meena(University of Rajasthan)0000-0001-9035-7561
Deo Brat Ojha(University of Rajasthan)0000-0001-7239-2646
Pages
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Publication Date
2026-10-06
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Optimality conditions of these functions in mathematical programming problem are obtained.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we establish a new class of $E$-convexity, namely $\alpha$-pre-$E$-convexity.
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Key Findings & Data:We define $\alpha$-pre-$E$-convex function (need not $E$-convex function), $\alpha$-prepseudo-$E$-convex function and discuss some properties of $\alpha$-pre-$E$-convex functions.
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Conclusion & Impact:Optimality conditions of these functions in mathematical programming problem are obtained.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$E$-convex function · $\alpha$-pre-$E$-convex function · $\alpha$-prepseudo-$E$-convex function

Abstract

In this paper, we establish a new class of $E$-convexity, namely $\alpha$-pre-$E$-convexity. We define $\alpha$-pre-$E$-convex function (need not $E$-convex function), $\alpha$-prepseudo-$E$-convex function and discuss some properties of $\alpha$-pre-$E$-convex functions. We observe that the class of $\alpha$-prepseudo-$E$-convex functions is more general than the class of $\alpha$-pre-$E$-convex functions. We also introduce the class of $\alpha$-$E$-convex functions which we prove it is equivalent to the class of differentiable $\alpha$-pre-$E$-convex functions. Optimality conditions of these functions in mathematical programming problem are obtained.

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Cite This Article

Meena, S., Ojha, D. B. (2026). $\alpha$-PRE-$E$-CONVEX AND $\alpha$-$E$-CONVEX FUNCTIONS WITH APPLICATIONS TO MATHEMATICAL PROGRAMMING. TWMS Journal of Applied and Engineering Mathematics, Volume: 16 Issue: 10. https://ajindex.com/articles/1604187

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