Mathematics and Statistics Vol. 9(1), pp. 59 - 64
DOI: 10.13189/ms.2021.090110
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Fixed Point Theorems in Complex Valued Quasi b-Metric Spaces for Satisfying Rational Type Contraction

J. Uma Maheswari , A. Anbarasan ^*, M. Ravichandran
Department of Mathematics, St. Joseph’s College (Autonomous), Tiruchirappalli - 620 002, India

ABSTRACT

The notion of complex valued metric spaces proved the common fixed point theorem that satisfies rational mapping of contraction. In the contraction mapping theory, several researchers demonstrated many fixed-point theorems, common fixed-point theorems and coupled fixed-point theorems by using complex valued metric spaces. The idea of b-metric spaces proved the fixed point theorem by the principle of contraction mapping. The notion of complex valued b-metric spaces, and this metric space was the generalization of complex valued metric spaces. They explained the fixed point theorem by using the rational contraction. In the metric spaces, we refer to this metric space as a quasi-metric space, the symmetric condition d(x, y) = d(y, x) is ignored. Metric space is a special kind of space that is quasi-metric. The Quasi metric spaces were discussed by many researchers. Banach introduced the theory of contraction mapping and proved the theorem of fixed points in metric spaces. We are now introducing the new notion of complex quasi b-metric spaces involving rational type contraction which proved the unique fixed point theorems with continuous as well as non-continuous functions. Illustrate this with example.

KEYWORDS
Fixed Point, Metric Space, Quasi Metric Space, Complex Valued Metric Space, Complex Valued Quasi b-metric Space

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] J. Uma Maheswari , A. Anbarasan , M. Ravichandran , "Fixed Point Theorems in Complex Valued Quasi b-Metric Spaces for Satisfying Rational Type Contraction," Mathematics and Statistics, Vol. 9, No. 1, pp. 59 - 64, 2021. DOI: 10.13189/ms.2021.090110.

(b). APA Format:
J. Uma Maheswari , A. Anbarasan , M. Ravichandran (2021). Fixed Point Theorems in Complex Valued Quasi b-Metric Spaces for Satisfying Rational Type Contraction. Mathematics and Statistics, 9(1), 59 - 64. DOI: 10.13189/ms.2021.090110.