A generalization of Matkowski’s fixed point theorem and Istrăţescu’s fixed point theorem concerning convex contractions

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.

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

Annales Mathematicae Silesianae ◽

10.2478/amsil-2021-0005 ◽

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.

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Subordinate Semimetric Spaces and Fixed Point Theorems

Journal of Mathematics ◽

10.1155/2018/7856594 ◽

2018 ◽

Vol 2018 ◽

pp. 1-5 ◽

Cited By ~ 1

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.

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A generalization of Istrățescu’s fixed point theorem for convex contractions

Fixed Point Theory ◽

10.24193/fpt-ro.2017.2.55 ◽

2017 ◽

Vol 18 (2) ◽

pp. 689-702 ◽

Cited By ~ 4

Author(s):

Radu Miculescu ◽

◽

Alexandru Mihail ◽

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Convex Contractions

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Iterated Function Systems Consisting of Generalized Convex Contractions in the Framework of Complete Strong b-metric Spaces

Annals of West University of Timisoara - Mathematics and Computer Science ◽

10.1515/awutm-2017-0018 ◽

2017 ◽

Vol 55 (2) ◽

pp. 119-142

Author(s):

Flavian Georgescu

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Metric Space ◽

Existence And Uniqueness ◽

Metric Spaces ◽

Iterated Function Systems ◽

Iterated Function ◽

Convex Contractions

AbstractThe concept of generalized convex contraction was introduced and studied by V. Istrăţescu and the notion ofb-metric space was introduced by I. A. Bakhtin and S. Czerwik. In this paper we combine these two elements by studying iterated function systems consisting of generalized convex contractions on the framework ofb-metric spaces. More precisely we prove the existence and uniqueness of the attractor of such a system providing in this way a generalization of Istrăţescu’s convex contractions fixed point theorem in the setting of complete strongb-metric spaces.

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A NEW NONLINEAR FRACTAL INTERPOLATION FUNCTION

Fractals ◽

10.1142/s0218348x17500633 ◽

2017 ◽

Vol 25 (06) ◽

pp. 1750063 ◽

Cited By ~ 14

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.

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