ON *-BOUNDEDNESS AND *-LOCAL BOUNDEDNESS OF NON-NEWTONIAN SUPERPOSITION OPERATORS IN c_(0,α) AND c_α TO l_(1,β)

Authors : Fatmanur ERDOGAN, Birsen SAĞIR DUYAR

Pages : 241-251

Doi:10.33773/jum.954104

View : 17 | Download : 6

Publication Date : 2021-07-31

Article Type : Research Paper

Abstract :Many investigations have been made about of Non-Newtonian calculus and superposition operators until today. Non-Newtonian superposition operator was defined by Sağır and Erdoğan in [9]. In this study, we have defined *- boundedness and *-locally boundedness of operator. We have proved that the non-Newtonian superposition operator $_{N}P_{f}:c_{_{0,\alpha }}\rightarrow \ell _{1,\beta }$ is *-locally bounded if and only if f satisfies the condition insert ignore into journalissuearticles values(NA₂′);. Then we have shown that the necessary and sufficient conditions for the *-boundedness of $% _{N}P_{f}:c_{_{0,\alpha }}\rightarrow \ell _{1,\beta }$ . Finally, the similar results have been also obtained for $_{N}P_{f}:c_{\alpha }\rightarrow \ell _{1,\beta }$ .
Keywords : Boundedness, local boundedness, non Newtonian superposition operator, non Newtonian sequence spaces