On Reverse and Generalized of Bellman Type Inequality

Year 2024, , 567 - 573, 27.06.2024

Necmettin Alp

https://doi.org/10.35414/akufemubid.1373603

Abstract

Bu çalışmanın amacı, önceki çalışmalar incelendikten sonra dışbükey ve integrallenebilir ve diferansiyellenebilir fonksiyonlar için ters Bellman tipi eşitsizliği elde etmektir. Bununla birlikte Bellman tipi eşitsizliğin genelleştirilmesinin ispatı yapılmıştır. Elde edilen ana sonuçlar yardımıyla dışbükey ve integrallenebilir, diferansiyellenebilir fonksiyonlar üzerine bazı özel durumlar elde edildi. Bu sonuçlar kullanılarak analitik olarak hesaplanması zor integraller için bir alt sınır elde dilmiştir

Keywords

konvekslik, eşitsizlikler, integral operatörü, bellman

On Reverse and Generalized of Bellman Type Inequality

Abstract

The aim of this work, to obtain reverse Bellman type inequality for convex and integrable-differentiable functions after examining the previous studies on the Bellman inequality and giving the results that are a source of inspiration for us. With that we proved the generalized of Bellman type
inequality. With the help of obtained main results, we have obtained some special cases on convex and integrable-differentiable functions. For convexity we have also included some examples to make these exercises more understandable. On the other hand, we have expressed with examples
to obtain a lower bound for hard integrals.

Keywords

convexity, inequalities, integral operator, bellman

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