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

Year 2021, , 241 - 251, 31.07.2021

Fatmanur Erdogan , Birsen Sağır Duyar

https://doi.org/10.33773/jum.954104

Cited By: 1

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 (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.

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