A structure of spaces using the notion of $\Delta$-operator method


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Authors

  • Abdul Ganie Saudi Electronic Universtiy

Abstract

The focus of the study in the this paper is to introduce the space $\mathcal{L}_s^\vartheta \left( p,\Delta_g^w \right)$. The completeness property will be determined. Various topological properties will be enlightened.

References

S. Banach and S. Saks, Sur la convergence forte dans les champs Lp, Studia Math. 2 (1930), 51–57.

J.A. Clarkson, Uniformly convex spaces, Trans Amer Math Soc. 40 (1936), 396–414.

Y. Cui, H. Hudzik H N. Petrot , S. Suantai and A. Szymaszkiewicz, Basic topological and geometric properties of

Cesàro-orlicz spaces, Proc Indian Acad Sci. (Math Sci.), 115(4) (2005), 461–476.

M. Et, Generalized Cesàro difference sequence spaces of non-absolute type involving lacunary sequences. Appl Math

Comput. 219(17) (2013), 9372–9376.

M. Et and R. Çolak, On some generalized difference sequence spaces, Soochow J. Math. 21 (1995), 377–386.

M. Et and A. Esi, On Köthe Toeplitz duals of generalized difference sequence spaces, Bull. Malaysian Math. Sc. Soc.

(2)23 (2000), 25–32.

D. Fathima and A. H. Ganie, On some new scenario of Δ-spaces, J. Nonlinear Sci. Appl. 14 (2021), 163–167.

C. Franchetti, Duality mapping and homeomorphisms in banach theory, in proceedings of researchworkshop on

banach spaces theory. University of Lowa. 1981.

A. R. Freedman, J. J. Sember and M. Raphael Some cesaro-type summability spaces. Proc Lond Math Soc. 37(3) (1978),

–520.

V. Karakaya, Some geometric properties of sequence spaces involving lacunary sequence. J Inequal Appl. Article ID

(2007), 1–8.

M. Karakas, M. Et, and V. Karakaya, Some geometric properties of a new difference sequence space involving lacunary

sequences. Acta Math Sci Ser. B Engl Ed. 33(6) (2013), 1711–1720.

H. Kizmaz, On certain sequence spaces. Canad Math Bull. 24(1) (1981), 169–176.

M. Mursaleen, R. Cólak and M. Et, some geometric lnequalities in a new banach sequence space. J Inequal Appl.

Article ID 86757 (2007), 1–6.

M. Mursaleen, A. H. Ganie, N. A. Sheikh, New type of generalized difference sequence space of non-absolute type and

some matrix transformations, Filomat. 28 (2014), 1381–1392.

Z. Opial, Weak convergence of the sequence of the successive approximations for non expansive mappings.Bull

AmerMath Soc. 73 (1967) 591–597.

M. Ozturk and M. Basarir, On k-NUC property in some sequence spaces involving lacunary sequence. Thai J. Math.

(1) (2007), 127–136.

N. Petrot and S. Suantai, Some geometric properties in orlicz-ces‘aro spaces. Sci Asia. 31 (2005), 173–177.

B. Pierre, Probability theory and stochastic processes, Springer Nature Switzerlang, April, 2020.

S. Prus, Banach spaces with uniform opial property. Nonlinear Anal Theory Appl. 18(8) (1992), 697–704.

S. Rolewicz, On-uniform convexity and drop property. Studia Math. 87(2) (1987), 181–191.

J. S. Shiue, Cesàro sequence spaces. Tamkang J. Math. 1 (1970), 143–150.

S. Suantai, On some convexity properties of generalized cesaro sequence space. Georgian Math J. 10 (2003), 193–200.

B. C. Tripathy, A. Esi, A new type of difference sequence spaces, Int. J. Sci. Technol. 1 (2006), 11–14.

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Published

2024-11-23

How to Cite

Ganie, A. (2024). A structure of spaces using the notion of $\Delta$-operator method. Results in Nonlinear Analysis, 7(4), 115–122. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/247