Convergence Theorems for Uncertain Variable Sequences

2014 ◽  
Vol 22 (04) ◽  
pp. 627-639 ◽  
Author(s):  
Jianrong Wu ◽  
Yang Xia
Keyword(s):  
Uncertain Variable ◽  
Convergence Theorems ◽  
Convergence In Measure ◽  
Convergence Almost Surely

For uncertain variable sequences, conditions of convergences such as Cauchy convergence in measure, convergence almost surely and convergence uniformly almost surely are given. Consequently, the relationships among convergences of uncertain variable sequences are shown. These results have not been proposed in literature so far.

Convergence of Complex Uncertain Double Sequences

2020 ◽  
Vol 16 (03) ◽  
pp. 447-459 ◽  
Author(s):  
Debasish Datta ◽  
Binod Chandra Tripathy
Keyword(s):  
Complex Numbers ◽  
Convergence In Distribution ◽  
Double Sequences ◽  
Convergence In Measure ◽  
Uncertain Variables ◽  
Mean Convergence ◽  
Model Complex ◽  
Uncertainty Space ◽  
Convergence Almost Surely ◽  
Convergence In Mean

Complex uncertain variables are measurable functions from an uncertainty space to the set of complex numbers and are used to model complex uncertain quantities. This paper introduces the convergence concepts of convergence almost surely (a.s.), convergence in measure, convergence in mean, convergence in distribution and convergence uniformly almost surely complex uncertain double sequences. In addition, relationships among the introduced classes of sequences have been introduced.

SOME PROPERTIES OF CONTINUOUS UNCERTAIN MEASURE

2009 ◽  
Vol 17 (03) ◽  
pp. 419-426 ◽  
Author(s):  
XIN GAO
Keyword(s):  
Uncertainty Theory ◽  
Uncertain Variable ◽  
Expected Value ◽  
Critical Values ◽  
Uncertain Measure ◽  
Uncertainty Distribution ◽  
Convergence Theorems ◽  
Basic Properties

In this paper, we discuss some properties in uncertainty theory when uncertain measure is continuous. Firstly, the judgement conditions of continuous uncertain measure are proposed. Secondly, basic properties of uncertainty distribution and critical values of uncertain variable are proved. Finally, the convergence theorems for expected value are discussed.

Statistical Convergence of Complex Uncertain Sequences

2017 ◽  
Vol 13 (03) ◽  
pp. 359-374 ◽  
Author(s):  
Binod Chandra Tripathy ◽  
Pankaj Kumar Nath
Keyword(s):  
Statistical Convergence ◽  
Complex Numbers ◽  
Convergence In Distribution ◽  
Convergence In Measure ◽  
Uncertain Variables ◽  
Model Complex ◽  
Uncertainty Space ◽  
Convergence Almost Surely ◽  
Decomposition Theorems ◽  
Convergence In Mean

Complex uncertain variables are measurable functions from an uncertainty space to the set of complex numbers and are used to model complex uncertain quantities. This paper introduces the statistical convergence concepts of complex uncertain sequences: statistical convergence almost surely (a.s.), statistical convergence in measure, statistical convergence in mean, statistical convergence in distribution and statistical convergence uniformly almost surely (u.a.s.) In addition, decomposition theorems and relationships among them are discussed.

STRONG AND Δ - CONVERGENCE THEOREMS USING MODIFIED PROXIMAL POINT ALGORITHM IN CAT(0) SPACES

2018 ◽  
Vol 7 (2) ◽  
pp. 8
Author(s):  
KUMAR DAS APURVA ◽  
DHAR DIWAN SHAILESH ◽  
DASHPUTRE SAMIR ◽  
◽  
◽  
...  
Keyword(s):  
Proximal Point Algorithm ◽  
Proximal Point ◽  
Convergence Theorems

Convergence theorems for total asymptotically nonexpansive single-valued and quasi nonexpansive multi-valued mappings in hyperbolic spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Preeyalak Chuadchawna ◽  
Ali Farajzadeh ◽  
Anchalee Kaewcharoen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Uniformly Convex Hyperbolic Space

Abstract In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result.

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