Fixed point results in α, β partial b-metric spaces using C-contraction type mapping and its generalization

Banach contraction mapping has main role in nonlinear analysis courses and has been modified to get new kind of generalizations in some abstract spaces to produce many fixed point theory. Fixed point theory has been proved in partial metric spaces and b-metric spaces as generalizations of metric spaces to obtain new theorems. In addition, using modified of contraction mapping we get some fixed point that have been used to solve differential equations or integral equations, and have many applications. Therefore, this area is actively studied by many researchers. The goal of this article is present and prove some fixed point theorems for extension of contraction mapping in α, β partial b-metric spaces. In this research, we learn about notions of b-metric spaces and partial metric that are combined to generated partial b-metric spaces from many literatures. Afterwards, generalizations are made to get α, β partial b-metric spaces. Using the properties of convergence, Cauchy sequences, and notions of completeness in α, β partial b-metric spaces, we prove some fixed point theorem. Fixed point theory that we generated used C-contraction mapping and its generalizations with some conditions. Existence and uniqueness of fixed point raised for some restrictions of α, β conditions. Some corollaries of main results are also proved. Our main theorems extend and increase some existence in the previous results.©2022 JNSMR UIN Walisongo. All rights reserved

Fixed point results in α, β partial b-metric spaces using C-contraction type mapping and its generalization

Banach contraction mapping has main role in nonlinear analysis courses and has been modified to get new kind of generalizations in some abstract spaces to produce many fixed point theory. Fixed point theory has been proved in partial metric spaces and b-metric spaces as generalizations of metric spaces to obtain new theorems. In addition, using modified of contraction mapping we get some fixed point that have been used to solve differential equations or integral equations, and have many applications. Therefore, this area is actively studied by many researchers. The goal of this article is present and prove some fixed point theorems for extension of contraction mapping in α, β partial b-metric spaces. In this research, we learn about notions of b-metric spaces and partial metric that are combined to generated partial b-metric spaces from many literatures. Afterwards, generalizations are made to get α, β partial b-metric spaces. Using the properties of convergence, Cauchy sequences, and notions of completeness in α, β partial b-metric spaces, we prove some fixed point theorem. Fixed point theory that we generated used C-contraction mapping and its generalizations with some conditions. Existence and uniqueness of fixed point raised for some restrictions of α, β conditions. Some corollaries of main results are also proved. Our main theorems extend and increase some existence in the previous results.©2022 JNSMR UIN Walisongo. All rights reserved

Fixed point results in α, β partial b-metric spaces using C-contraction type mapping and its generalization

Banach contraction mapping has main role in nonlinear analysis courses and has been modified to get new kind of generalizations in some abstract spaces to produce many fixed point theory. Fixed point theory has been proved in partial metric spaces and b-metric spaces as generalizations of metric spaces to obtain new theorems. In addition, using modified of contraction mapping we get some fixed point that have been used to solve differential equations or integral equations, and have many applications. Therefore, this area is actively studied by many researchers. The goal of this article is present and prove some fixed point theorems for extension of contraction mapping in α, β partial b-metric spaces. In this research, we learn about notions of b-metric spaces and partial metric that are combined to generated partial b-metric spaces from many literatures. Afterwards, generalizations are made to get α, β partial b-metric spaces. Using the properties of convergence, Cauchy sequences, and notions of completeness in α, β partial b-metric spaces, we prove some fixed point theorem. Fixed point theory that we generated used C-contraction mapping and its generalizations with some conditions. Existence and uniqueness of fixed point raised for some restrictions of α, β conditions. Some corollaries of main results are also proved. Our main theorems extend and increase some existence in the previous results.©2022 JNSMR UIN Walisongo. All rights reserved

ANALISIS KESALAHAN FAKTA DAN KESALAHAN KONSEP MAHASISWA DALAM MENYELESAIKAN SOAL GEOMETRI ANALITIK RUANG

This study aims to describe both fact and concept error of students in solving space analytic geometry problems. The subjects of this research are two students of Mathematics Department of Universitas Negeri Makassar. Each of them represents for each error (fact and concept errors). The collecting data were employed by using space analytic geometric tests and depth-interview. Interview guidelines and researcher were as research instruments. Data were qualitatively analyzed, using three stages of analysis: data reduction, data display and concluding. The main findings of this research are (1) the subject of fact error made mistakes in writing vector symbols, (2) the subjects of concept error made mistakes in identifying an equation (plane equation or line equation), since his focus was only in the number of variables of the equation.Keywords: fact error, concept error, space analytic geometry

Analisis Kesalahan Operasi dan Kesalahan Prinsip Mahasiswa dalam Menyelesaikan Soal Geometri Analitik Ruang

Abstrak: Studi ini ditujukan untuk menggambarkan kesalahan operasi dan kesalahan prinsip mahasiswa dalam menyelesaikan soal-soal geometri analitik ruang. Subjek dari penelitian ini terdiri dari dua mahasiswa Jurusan Matematika Universitas Negeri Makassar. Setiap kesalahan diwakili dengan satu mahasiswa sebagai subjek penelitian. Pengumpulan data dilakukan dengan menggunakan tes dan wawancara mendalam. Instrumen penelitian ini adalah pedoman wawancara dan peneliti. Data dianalisis secara kualitatif, dengan menggunakan tiga tahapan analisis: reduksi data, penyajian data, dan penarikan kesimpulan. Hasil penelitian ini adalah (1) subjek untuk kesalahan operasi salah dalam pengoperasian aritmatika bentuk aljabar yaitu subjek lupa mengoperasikan sebagian dari bilangan atau variabel; dan (2) subjek untuk kesalahan prinsip menganggap bahwa vektor normal setiap bidang sisi tegak prisma saling tegak lurus. Abstract: This study aims to describe both operation and principle errors of students in solving space analytic geometry problems. The subjects of this research are two students of Mathematics Department of Universitas Negeri Makassar. Each of error (operation and principle errors) is represented by a student. The collecting data were employed by using a tests and a depth-interview. Instruments of this research are Interview guidelines and researcher. Data were qualitatively analyzed, using three stages of analysis: data reduction, data display and concluding. The results of this research are (1) the subject of operation error made mistakes in operating of algebra forms such as forgetting to operate a part of number or variable (2) the subjects of principle error assume that the normal vectors of each side of prisme are perpendicular

Teorema Titik Tetap untuk Pemetaan Bernilai Himpunan pada Subset dari Ruang b-Metrik

Abstrak.  Tulisan ini membahas tentang teorema titik tetap untuk pemetaan bernilai himpuanan dengan domain berupa subset dari suatu ruang b-metrik. Hasil yang diperoleh merupakan pengembangan dari hasil yang telah diperoleh pada literatur terdahulu. Kata kunci: b-metrik, pemetaan bernilai himpuan, teorema titik tetap.   Abstract.  This paper study about fixed point theorem for set-valued maps where its domain is subset of a b-metric space. The result is improvement from the literature. Keywords: b-metric, set-valued maps, fixed point theorem