Existence and Iterative Approximation of Hybrid Best Proximity Points for Set-Valued Mappings*

2021 ◽  
pp. 1-19
Author(s):  
Shihuang Hong ◽  
Menghao Shao ◽  
Xinggang Luo
Keyword(s):  
Iterative Approximation ◽  
Best Proximity Points ◽  
Set Valued Mappings

Best proximity points for a new type of set-valued mappings

2019 ◽  
Vol 69 (6) ◽  
pp. 1395-1402
Author(s):  
Aleksandar Kostić
Keyword(s):  
Fixed Point ◽  
Point Theorem ◽  
Best Proximity Point ◽  
Contractive Condition ◽  
Best Proximity Points ◽  
New Type ◽  
Set Valued Mappings

Abstract In this paper, we introduce a new type of set-valued mappings satisfying a contractive condition involving SR-functions. Then we prove a best proximity point theorem concerning the aforementioned mappings. Some new best proximity and fixed point results are obtained as consequences. An example is provided to support the theory.

Electron Microscopy and image reconstruction reveal the structural basis for spectrin's elastic properties

1992 ◽  
Vol 50 (1) ◽  
pp. 510-511
Author(s):  
Amy M. McGough ◽  
Robert Josephs
Keyword(s):  
Electron Microscopy ◽  
Elastic Properties ◽  
Conformational Changes ◽  
Quaternary Structure ◽  
Three Dimensional ◽  
Membrane Skeleton ◽  
Projection Algorithm ◽  
Structural Basis ◽  
Iterative Approximation ◽  
Membrane Skeletons

The remarkable deformability of the erythrocyte derives in large part from the elastic properties of spectrin, the major component of the membrane skeleton. It is generally accepted that spectrin's elasticity arises from marked conformational changes which include variations in its overall length (1). In this work the structure of spectrin in partially expanded membrane skeletons was studied by electron microscopy to determine the molecular basis for spectrin's elastic properties. Spectrin molecules were analysed with respect to three features: length, conformation, and quaternary structure. The results of these studies lead to a model of how spectrin mediates the elastic deformation of the erythrocyte.Membrane skeletons were isolated from erythrocyte membrane ghosts, negatively stained, and examined by transmission electron microscopy (2). Particle lengths and end-to-end distances were measured from enlarged prints using the computer program MACMEASURE. Spectrin conformation (straightness) was assessed by calculating the particles’ correlation length by iterative approximation (3). Digitised spectrin images were correlation averaged or Fourier filtered to improve their signal-to-noise ratios. Three-dimensional reconstructions were performed using a suite of programs which were based on the filtered back-projection algorithm and executed on a cluster of Microvax 3200 workstations (4).

C-class functions and pair (F,h) Upper class on common best proximity points results for new proximal C-contraction mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3459-3471
Author(s):  
A.H. Ansari ◽  
Geno Jacob ◽  
D. Chellapillai
Keyword(s):  
Best Proximity Point ◽  
Upper Class ◽  
Best Proximity Points ◽  
Contraction Mappings ◽  
Common Best Proximity Point

In this paper, using the concept of C-class and Upper class functions we prove the existence of unique common best proximity point. Our main result generalizes results of Kumam et al. [[17]] and Parvaneh et al. [[21]].

The minimum zone fitting and error evaluation for the logarithmic curve based on geometry optimization approximation algorithm

2019 ◽  
Vol 41 (15) ◽  
pp. 4380-4386
Author(s):  
Tu Xianping ◽  
Lei Xianqing ◽  
Ma Wensuo ◽  
Wang Xiaoyi ◽  
Hu Luqing ◽  
...  
Keyword(s):  
Approximation Algorithm ◽  
Evaluation Method ◽  
Geometry Optimization ◽  
Reference Points ◽  
Approximation Technique ◽  
Error Evaluation ◽  
Iterative Approximation ◽  
Logarithmic Curve ◽  
Normal Distance ◽  
Minimum Zone

The minimum zone fitting and error evaluation for the logarithmic curve has important applications. Based on geometry optimization approximation algorithm whilst considering geometric characteristics of logarithmic curves, a new fitting and error evaluation method for the logarithmic curve is presented. To this end, two feature points, to serve as reference, are chosen either from those located on the least squares logarithmic curve or from amongst measurement points. Four auxiliary points surrounding each of the two reference points are then arranged to resemble vertices of a square. Subsequently, based on these auxiliary points, a series of auxiliary logarithmic curves (16 curves) are constructed, and the normal distance and corresponding range of values between each measurement point and all auxiliary logarithmic curves are calculated. Finally, by means of an iterative approximation technique consisting of comparing, evaluating, and changing reference points; determining new auxiliary points; and constructing corresponding auxiliary logarithmic curves, minimum zone fitting and evaluation of logarithmic curve profile errors are implemented. The example results show that the logarithmic curve can be fitted, and its profile error can be evaluated effectively and precisely using the presented method.

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