Some geometrical properties and fixed point theorems in Orlicz spaces

Khamsi, Mohamed A.; Kozƚowski, Wojciech M.; Chen, Shutao

doi:10.1016/0022-247x(91)90009-o

Cited by 38 publications

(32 citation statements)

References 9 publications

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“…there holds f = g. Note that in [11], the authors proved that in Orlicz spaces over a finite, atomless measure space, both conditions (UC) and (UUC) are equivalent. Typical examples of Orlicz functions that do not satisfy the Δ 2 condition but are uniformly convex are: 1 (t) = e |t| -|t|-1 and ϕ 2 (t) = e t 2 − 1 .…”

Section: Penot Compactness Of Admissible Setsmentioning

confidence: 99%

One-local retract and common fixed point in modular function spaces

Al-Mezel

Al-roqi

Khamsi

2012

Fixed Point Theory Appl

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In this paper, we introduce and study the concept of one-local retract in modular function spaces. In particular, we prove that any commutative family of r-nonexpansive mappings defined on a nonempty, r-closed and r-bounded subset of a modular function space has a common fixed point provided its convexity structure of admissible subsets is compact and normal. MSC: Primary 47H09; Secondary 46B20, 47H10.

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Section: Penot Compactness Of Admissible Setsmentioning

confidence: 99%

One-local retract and common fixed point in modular function spaces

Al-Mezel

Al-roqi

Khamsi

2012

Fixed Point Theory Appl

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“…But in the absence of the ∆ 2 -condition, we may still have (UC1) provided the Orlicz function is uniformly convex like ϕ 1 (t) = e |t| − |t| − 1 and ϕ 2 (t) = e t 2 − 1 [4,11,16].…”

Section: Definition 31 ([10]mentioning

confidence: 99%

Fixed point theorems in modular vector spaces

Abdou¹,

Khamsi²

2017

J. Nonlinear Sci. Appl.

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“…We begin by recalling the definitions of ρ-modulus of uniform convexity [9]. For any ε and any r > 0, the ρ-modulus of uniform convexity is defined by…”

Section: Uniformly Convex Modular Spacesmentioning

confidence: 99%

Uniformly Lipschitzian mappings in modular function spaces

Benavides

Khamsi

Samadi

2001

Nonlinear Analysis: Theory, Methods & Applications

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Let ρ be a convex modular function satisfying a ∆ 2 -type condition and L ρ the corresponding modular space. Assume that C is a ρ-bounded and ρ-a.e compact subset of L ρ and T : C → C is a k-uniformly Lipschitzian mapping. We proveis a geometrical coefficient of normal structure. We also show thatÑ(L ρ ) < 1 in modular Orlicz spaces for uniformly convex Orlicz functions.1991 Mathematics subject classification: Primary 46E30; Secondary 47H09, 47H10.

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Some geometrical properties and fixed point theorems in Orlicz spaces

Cited by 38 publications

References 9 publications

One-local retract and common fixed point in modular function spaces

One-local retract and common fixed point in modular function spaces

Fixed point theorems in modular vector spaces

Uniformly Lipschitzian mappings in modular function spaces

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