Proceeding2562

389 การประชุมวิชาการระดับชาติมหาวิทยาลัยทักษิณ ครั้งที่ 29 ประจ�ำปี 2562 วิจัยและนวัตกรรมเพื่อการพัฒนาที่ยั่งยืน A Fixed point theorem in a generalized b-metric space Yaowaluck Khongtham 1* Abstract Introduction : Fixed point theory in metric space has been found a lot of applications in different branches of Mathematics. Several fixed point theories have been shown a unique existence with various different contrac- tion mappings such as Banach contraction mapping, Chatterjea’s contraction mapping, and Hardy and Rogers’ contraction mapping, etc. Bakhtin and Czerwik introduced the concept of b-metric spaces as a generalization of a metric space. Several researches have dealt with fixed point theories for various contraction mappings in b-metric spaces and its applications. Recently, Kamran et al. introduced a generalization of a b-metric space, gave some fixed point theorems and gave an application for the existence solution of Fredholm integral equa- tion. Objective : The purpose of this paper is to study the existence of a fixed point in a generalized b – metric space by using the Hardy and Rogers’ contraction mapping. Methods : We studied definitions, convergences, and fixed point theories in generalized b-metric. Then we established and proved a new fixed point theorem using the Hardy and Rogers’ contraction mapping in a gen- eralized b-metric. Result : Our fixed point theorem using the Hardy and Rogers’ contraction mapping in a generalized b-metric has a unique fixed point. Conclusion : The fixed point theorem which be established in this paper is an extension of theorem which be presented by Kamran et al. It also is a generalization of many pre-existing theorems in metric space and b–met- ric spaces. Keywords : Fixed point theory, b-Metric space, Generalized b-metric space