ÖzBu çalışmada, geometrik hesap tarzına göre Lebesgue dizi uzayı tanımlandı. İhtiyaç duyulan bazı eşitsizlikler geometrik hesap tarzına göre elde edildi. Bu eşitsizlikler yardımıyla geometrik hesap tarzına göre Lebesgue dizi uzayının konvekslik, kesin konvekslik gibi bazı geometrik özellikleri incelendi.

Many investigations have been made about of non-Newtonian calculus and superposition operators until today. Non-Newtonian superposition operator was defined by Sagır and Erdogan in [9]. In this study, we have defined *-boundedness and *-locally boundedness of operator. We have proved that the non-Newtonian superposition operator N P f : c 0,α → 1,β is *-locally bounded if and only if f satisfies the condition (N A 2 ). Then we have shown that the necessary and sufficient conditions for the *-boundedness of N P f : c 0,α → 1,β . Finally, the similar results have been also obtained for N P f : cα → 1,β .

Many studies have been done on superposition operators and non-Newtonian calculus from past to present. Sağır and Erdoğan defined Non-Newtonian superposition operators and characterized them on some sequence spaces. Also they examined *-boundedness and *locally boundedness of Non-Newtonian superposition operators c0,α and cα to l1,β. In this study, we define *-continuity and *-uniform continuity of operator. We have proved that the necessary and sufficient conditions for the *-continuity of the non-Newtonian superposition operator c0,α to l1,β. Then we examined the relationship between the *-uniform continuity and the *-boundedness of the non-Newtonian superposition operator. Also, the similar results have been researched for the Non-Newtonian superposition operator cα to l1,β.