A NEW NONLINEAR BIVARIATE FRACTAL INTERPOLATION FUNCTION

Fractals ◽  
2018 ◽  
Vol 26 (04) ◽  
pp. 1850054 ◽  
Author(s):  
SONG-IL RI
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fractal Interpolation ◽  
Interpolation Function ◽  
Rectangular Grid ◽  
Fractal Interpolation Function ◽  
Fractal Interpolation Surface ◽  
Matkowski’S Fixed Point Theorem

In this paper, we present a new nonlinear bivariate fractal interpolation function (FIF) by using the Matkowski’s fixed point theorem and the Rakotch contraction. In particular, we give a new nonlinear fractal interpolation surface (FIS) on a rectangular grid. Our technique is different from the methods presented in the literature.

A NEW NONLINEAR FRACTAL INTERPOLATION FUNCTION

Fractals ◽  
2017 ◽  
Vol 25 (06) ◽  
pp. 1750063 ◽  
Author(s):  
SONGIL RI
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Shape Representation ◽  
Fractal Interpolation ◽  
Interpolation Function ◽  
Practical Applications ◽  
Fractal Interpolation Function ◽  
Matkowski’S Fixed Point Theorem

In this paper, we propose a new nonlinear fractal interpolation function by using the Matkowski’s fixed point theorem and Rakotch contraction. The aim of this paper is to create a method that is accurate and suitable for practical applications such as shape representation. Our technique is different from the methods presented in the previous literatures.

NONLINEAR RECURRENT HIDDEN VARIABLE FRACTAL INTERPOLATION CURVES WITH FUNCTION VERTICAL SCALING FACTORS

Fractals ◽  
2020 ◽  
Vol 28 (06) ◽  
pp. 2050096
Author(s):  
JINMYONG KIM ◽  
HAKMYONG MUN
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Iterated Function Systems ◽  
Vertical Scaling ◽  
Fractal Interpolation ◽  
Scaling Factors ◽  
Hidden Variable ◽  
Iterated Function

In this paper, we present a construction of new nonlinear recurrent hidden variable fractal interpolation curves. In order to get new fractal curves, we use Rakotch’s fixed point theorem. We construct recurrent hidden variable iterated function systems with function vertical scaling factors to generate more flexible fractal interpolation curves. We also give an illustrative example to demonstrate the effectiveness of our results.

scholarly journals A New Proof and Consequences of the Fixed Point Theorem of Matkowski

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Eugeniusz Barcz
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
The Fixed Point Theorem ◽  
Matkowski’S Fixed Point Theorem

Abstract In this work it was proved Matkowski’s fixed point theorem. The consequences of this theorem are also presented.

NEW NONLINEAR RECURRENT HIDDEN VARIABLE FRACTAL INTERPOLATION SURFACES

Fractals ◽  
2020 ◽  
Vol 28 (02) ◽  
pp. 2050038
Author(s):  
HYONJIN KIM ◽  
JINMYONG KIM ◽  
HAKMYONG MUN
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Iterated Function Systems ◽  
Vertical Scaling ◽  
Fractal Interpolation ◽  
Scaling Factors ◽  
Fractal Surfaces ◽  
Hidden Variable ◽  
Iterated Function

In this paper, we present the construction of new nonlinear recurrent hidden variable fractal interpolation surfaces (RHVFISs) with function vertical scaling factors. We use Rakotch’s fixed point theorem which is a generalization of Banach’s fixed point theorem to get new nonlinear fractal surfaces. We construct recurrent vector-valued iterated function systems (IFSs) with function vertical scaling factors on rectangular grids and generate flexible and diverse RHVFISs which are attractors of the IFSs. We also give an explicit example to show the effectiveness of obtained results.

scholarly journals Subordinate Semimetric Spaces and Fixed Point Theorems

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
José Villa-Morales
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Generalized Metric Space ◽  
Generalized Metric ◽  
Semimetric Space ◽  
Semimetric Spaces ◽  
Matkowski’S Fixed Point Theorem

We introduce the concept of subordinate semimetric space. Such notion includes the concept of RS-space introduced by Roldán and Shahzad; therefore the concepts of Branciari’s generalized metric space and Jleli and Samet’s generalized metric space are particular cases. For such spaces we prove a version of Matkowski’s fixed point theorem, and introducing the concept of q-contraction we get a fixed point theorem of Kannan-Ćirić type. Moreover, using such result we characterize complete subordinate semimetric spaces.

Altman's contractors and Matkowski's fixed point theorem

1981 ◽  
Vol 5 (10) ◽  
pp. 1061-1075 ◽  
Author(s):  
K.Balakrishna Reddy ◽  
P.V. Subrahmanyam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Matkowski’S Fixed Point Theorem

scholarly journals PERAN FAKTOR PENYEKALA PADA KONSTRUKSI INTERPOLASI FRAKTAL

2012 ◽  
Vol 7 (2) ◽  
Author(s):  
Marwan Marwan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Iterated Function System ◽  
Scaling Factor ◽  
Vertical Scaling ◽  
Necessary Condition ◽  
Affine Mapping ◽  
Fractal Interpolation Function ◽  
The Fixed Point Theorem

Abstrak: Telah diketahui bahwa suatu fungsi fraktal  yang menginterpolasi data  sedemikian hingga  untuk   dapat dikonstruksi dari suatu Sistem Fungsi Iterasi (SFI) berdasarkan teorema titik tetap pada pemetaan kontraktif. Dengan mengambil suatu bentuk pemetaan Affine, yang merupakan salah satu bentuk pemetaan kontraktif untuk SFI, dapat dibuktikan eksistensi atraktor SFI dimaksud yang tidak lain merupakan interpolan fraktal dari data terkait. Faktor penyekala  yang termuat di dalam pemetaan affine memegang peran sebagai syarat perlu eksistensi dan ketunggalan fungsi interpolasi fraktal suatu data. Syarat perlu tersebut berlaku pada batasan nilai . Kata kunci : interpolan fraktal, SFI, teorema titik tetap, pemetaan affine, faktor penyekala. Abstract: It is known that a fractal functions   that interpolated the data  such that ,  can be constructed from an Iterated Function System (IFS) based on The Fixed Point Theorem on contractive mappings. By taking a certain Affine Mapping, which is a form of contractive mapping on IFS, the existence of IFS’ attractor can be proven as the  fractal interpolan of related data. The vertical scaling factor  contained in the affine mapping role as a necessary condition of existence and uniqueness of a fractal interpolation function data. The necessary condition of   is on the interval . Keywords :    fractal interpolan, IFS, The Fixed Point Theorem, Affine Mapping,  vertical scaling factor)

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