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

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

A NEW NONLINEAR BIVARIATE FRACTAL INTERPOLATION FUNCTION

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.

Subordinate Semimetric Spaces and Fixed Point Theorems

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.

A NEW NONLINEAR FRACTAL INTERPOLATION FUNCTION

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.