ON *-BOUNDEDNESS AND *-LOCAL BOUNDEDNESS OF NON-NEWTONIAN SUPERPOSITION OPERATORS IN c_(0,α) AND c_α TO l_(1,β)
ON *-BOUNDEDNESS AND *-LOCAL BOUNDEDNESS OF NON-NEWTONIAN SUPERPOSITION OPERATORS IN c_(0,α) AND c_α TO l_(1,β)
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.,
___
- M. Grossman and R. Katz, "Non-Newtonian Calculus", 1st ed., Lee Press, Pigeon Cove Massachussets, (1972).
- F. Dedagich and P.P. Zabreiko, "Operator superpositions in the spaces lp ", Sibirskii Matematicheskii Zhurnal, 28, 86-98, (1987).
- P. Tainchai, "Boundedness of superposition operators on some sequence spaces", Master of Sciences Dissertation, Graduate School of Chiang Mai University, 40, Thailand,(1996).
- A. Sama-ae, "Boundedness of superposition operators on the sequence spaces of Maddox", Master of Sciences Dissertation, Graduate School of Chiang Mai University, 55, Thailand, (1997).
- A. F. Cakmak and F. Basar, "Some new results on sequence spaces with respect to non-Newtonian calculus", Journal of Inequalities and Applications, vol. 228, no.1, 1-17, (2012).
- B. Sagır and N. Gungor, "Locally Boundedness and Continuity of Superposition Operators on the Double Sequence Spaces Cr0", Journal of Computational Analysis and Applications, vol. 19(2), 365-377, (2015).
- C. Duyar and M. Erdogan, "On non-Newtonian real number series", IOSR Journal of Mathematics, vol. 12, iss. 6, ver. IV, 34-48, (2016).
- O. Ogur, "On characterization of boundedness of superposition operators on the Maddox space Cr0(p) of double sequences", New Trends in Mathematical Sciences, 4, 80-88, (2017).
- B. Sagır and F. Erdogan, "On Characterization of Non-Newtonian Superposition Operators in Some Sequence Spaces", Filomat, 33:9, 2601-2612, (2019).
- B. Sagır and F. Erdogan, "On Function Sequences and Series in the Non-Newtonian Calculus", Journal of Science and Arts, 4(49), 915-936, (2019).
- N. Gungor, "Some geometric properties of the non-Newtonian sequence spaces lp(N)", Mathematica Slovaca, vol. 70:3, 689-696, (2020).
- ISSN: 2618-5660
- Başlangıç: 2018
- Yayıncı: Gökhan ÇUVALCIOĞLU
Sayıdaki Diğer Makaleler
ON FUNCTION SPACES CHARACTERIZED BY THE WIGNER TRANSFORM
Fatmanur ERDOGAN, Birsen SAĞIR DUYAR
BLOW-UP RESULTS FOR A VISCOELASTIC PLATE EQUATION WITH DISTRIBUTED DELAY
Hazal YÜKSEKKAYA, Erhan PİŞKİN
GLOBAL NONEXISTENCE OF THE HIGHER ORDER KIRCHHOFF TYPE SYSTEM WITH LOGARITHMIC NONLINEARITIES
ON GENERALIZATIONS OF LOCALLY ARTINIAN SUPPLEMENTED MODULES
CONNECTEDNESS IN TEMPORAL INTUITIONISTIC FUZZY TOPOLOGY IN CHANG'S SENSE
C-PURE SUBMODULES AND C-FLAT MODULES
RULED SURFACE WITH CONSTANT SLOPE ACCORDING TO OSCULATING PLANE OF BASE CURVE IN GALILEAN 3- SPACE