A new solution to the Rhoades’ open problem with an application

We give a new solution to the Rhoades’ open problem on the discontinuity at fixed point via the notion of an S-metric. To do this, we develop a new technique by means of the notion of a Zamfirescu mapping. Also, we consider a recent problem called the “fixed-circle problem” and propose a new solution to this problem as an application of our technique.

ON THE FIXED-CIRCLE PROBLEM

In this paper, we focus on the geometric properties of fixed-points of a self-mapping and obtain new solutions to a recent problem called "fixed-circle problem" in the setting of an S-metric space. For this purpose, we develop various techniques by defining new contractive conditions and using some auxiliary functions. Furthermore, we present new examples to support our theoretical results.

Fixed-disc results on metric spaces

In this paper, we deal with the geometric properties of non-unique fixed points for self-mappings of a metric space (resp. an S-metric space). The fixed-disc (resp. fixed-circle) problem has been investigated in this setting. To obtain new fixed-disc results, we modify some known fixed-point techniques. Illustrative examples are also given to show the validity of our main results.

Students’ Mathematical Connection Error in Solving PISA Circle Problem

<p>The mathematical connection is one of the competencies in NCTM that students need to have. Mathematical connections can help students understand material and mathematical concepts easily. In addition, mathematical connections can help students in solving mathematical problems. Even so, mathematical connection errors are still made by some students. Mathematical connection errors made by students when solving geometry problems, especially about a circle. The purpose of this study is to describe the mathematical connection errors made by students in solving problems adapted from PISA problems focusing on circle material. This research method is descriptive-qualitative. Prospective subjects are 20 of 8th-grade students in one of the junior high schools in Malang who have studied about a circle. Based on the distribution of answers, two subjects were selected in this study. After going through the interview process, the data obtained in the form of work results and interview transcripts. Based on the results of research, mathematical connection errors made by research subjects in the form of not being able to use mathematics in mathematical problems; can't find connections between topics in mathematics; unable to understand the representation of concepts in mathematical problems, and draw relationships between procedures on mathematical problems</p>