id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
easat-3054	Habeeb, Nadia Abed ; Bhaya, Eman Samir 	Fractional integral Ostrowski inequality on L_P,0	2024	10	.pdf	application/pdf	3728	132	80	(𝑞+1)𝛼 𝑞 (12) Put (7) and (12) in (8), we get |(𝐼 − ℎ)𝛼𝑓(𝑥) + ℎ𝛼 𝑓(𝑎) + 𝑓(𝑏) 2𝛼 − Γ(1 + 𝛼) (𝑏 − 𝑎)𝛼 𝑎𝐼𝑏 ∝𝑓(𝑥)| ≤ 1 (𝑏 − 𝑎)𝛼 ( (𝛤(1 + 𝛼𝑞)) 𝛤(1 + (𝑞 + 1)𝛼) (𝑏(𝑞+1)𝛼 − 𝑎(𝑞+1)𝛼)) 1 𝑞 × ( 1 𝛤(1 + 𝛼) ) 1 𝑝 ‖𝑓𝛼‖𝑝 . [((𝑏 − ℎ ( 𝑏 − 𝑎 2 )) (𝑞+1)𝛼 − 𝑥(𝑞+1)𝛼) +(𝑥(𝑞+1)𝛼 − (𝑏 − ℎ ( 𝑏 − 𝑎 2 )) (𝑞+1)𝛼 )] = Γ(1 + 𝛼𝑞) Γ(1 + (𝑞 + 1)𝛼) (𝑏(𝑞+1)𝛼 − 𝑥(𝑞+1)𝛼) (11) Put (10) and(11) in (9), we get ( 1 Γ(1 + 𝛼) ∫|𝑝(𝑥, 𝑡)|𝑞(𝑑𝑥)𝛼 𝑏 𝑎 ) 1 𝑞 = [ Γ(1 + 𝛼𝑞) Γ(1 + (𝑞 + 1)𝛼) (𝑥(𝑞+1)𝛼 − 𝑎(𝑞+1)𝛼) + (𝑏(𝑞+1)𝛼 − 𝑥(𝑞+1)𝛼)] 1 𝑞 = ( Γ(1 + 𝛼𝑞) Γ(1 + (𝑞 + 1)𝛼) (𝑏(𝑞+1)𝛼 − 𝑎(𝑞+1)𝛼)) 1 𝑞 ≤ ( Γ(1 + 𝛼𝑞) Γ(1 + (𝑞 + 1)𝛼) ) 1 𝑞 (𝑏 − 𝑎)	cache/easat-3054.pdf	txt/easat-3054.txt