Simpson Type Integral Inequalities for Harmonic Convex Functions via Conformable Fractional Integrals

Abstract

Fractional integral operators are very useful in the field of mathematical analysis and optimization theory. The main aim of this investigation is to establish a new Simpson type conformable fractional integral equality for harmonically convex functions. Using this identity, some new results related to Simpson-like type conformable fractional integral inequalities are obtained. Then, some interesting conclusions are attained for some special cases of conformable fractional integrals when alpha = 1.

Keywords

• Simpson inequality
• Conformable fractional integral
• Harmonic convex

Conformable Kesirli İntegraller Aracılığıyla Harmonik Konveks Fonksiyonlar için Simpson Tipi İntegral Eşitsizlikleri

Abstract

Kesirli integral operatörleri matematiksel analiz ve optimizasyon teorisi alanlarında oldukça kullanışlıdır. Bu araştırmanın temel amacı harmonik konveks fonksiyonlar için yeni bir Simpson tipi conformable kesirli integral eşitliği kurmaktır. Bu eşitliği kullanarak Simpson tipi conformable kesirli integral eşitsizlikleri ile ilgili bazı yeni sonuçlar elde edildi. Daha sonra, 𝛼 = 1 olduğunda, conformable kesirli integrallerin bazı özel durumları için ilginç sonuçlara ulaşıldı.

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