Some geometric properties of the non-Newtonian sequence spaces lp(N)

2020 ◽  
Vol 70 (3) ◽  
pp. 689-696 ◽  
Author(s):  
Ni̇han Güngör
Keyword(s):  
Strict Convexity ◽  
Sequence Spaces ◽  
Uniform Convexity ◽  
Geometric Properties ◽  
Convexity Properties

AbstractIn this paper, we generalize the concepts of convexity, strict convexity and uniform convexity in the sense of non-Newtonian calculus. The main aim of this study is to obtain the non-Newtonian convexity, non-Newtonian strict convexity and non-Newtonian uniform convexity properties of the non-Newtonian sequence spaces lp(N).

scholarly journals Complex Convexity of Orlicz Modular Sequence Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Lili Chen ◽  
Deyun Chen ◽  
Yang Jiang
Keyword(s):  
Sequence Space ◽  
Extreme Points ◽  
Strict Convexity ◽  
Sequence Spaces ◽  
Uniform Convexity ◽  
Uniformly Convex ◽  
Strictly Convex ◽  
Modular Spaces

The concepts of complex extreme points, complex strongly extreme points, complex strict convexity, and complex midpoint locally uniform convexity in general modular spaces are introduced. Then we prove that, for any Orlicz modular sequence spacelΦ,ρ,lΦ,ρis complex midpoint locally uniformly convex. As a corollary,lΦ,ρis also complex strictly convex.

Some vector valued sequence spaces of Musielak-Orlicz functions and their operator ideals

2018 ◽  
Vol 68 (1) ◽  
pp. 115-134 ◽  
Author(s):  
Mohammad Mursaleen ◽  
Kuldip Raj
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Operator Ideals ◽  
Orlicz Sequence Space ◽  
Geometric Properties ◽  
Orlicz Functions ◽  
Opial Property ◽  
Uniform Opial Property ◽  
Vector Valued

AbstractIn the present paper we introduce generalized vector-valued Musielak-Orlicz sequence spacel(A,𝓜,u,p,Δr,∥·,… ,·∥)(X) and study some geometric properties like uniformly monotone, uniform Opial property for this space. Further, we discuss the operators ofs-type and operator ideals by using the sequence ofs-number (in the sense of Pietsch) under certain conditions on matrixA.

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