European Journal of Molecular & Clinical Medicine ISSN 2515-8260 Volume 07, Issue 09, 2020 3190 FIXED POINT THEOREMS FOR INTEGRAL TYPE F- CONTRACTIONS IN COMPLEX VALUED G B -METRIC SPACES Dr. A. Leema Maria Prakasam, Dr.A. Mary Priya Dharsini and Ms.A. Jennie Sebasty Pritha PG and Research Department of Mathematics Holy Cross College (Autonomous), Trichy-2 E-mail: leemamaria15@gmail.com Abstract: In this paper, we obtain a unique fixed point theorem of integral type F-contractions in complex valued G b -metrics paces. Keywords: G-metric space, F-contraction, weaklycompatible. 1 Introduction and Preliminaries In many branches of science, economics, computer science, engineering and the development of non-linear dynamics, the fixed point theory is one ofthe most important tool. In 1989, I. A. Bakhtin [1] introduced the contraction mapping principle in quasimetric spaces. In 2006, Mustafa and Sims introduced generalised metric spaces and extended fixed point theorems for contractive mappings in complete G-metric spaces. Abbas, Nazir and Vetro introduced common fixed point results for three maps in G-metricspaces.Vildan Uzturk introduced integral type F- contractions in partial metric spaces.In this paper, we obtain a unique fixed point theorem of integral type F-contractions in G- metric space which is generalised results of[6]. Definition 1.1 [4]Let X be a non-empty set and s ≥ 1 be a given real number. Suppose that a mapping G : X × X × X → ℂ satisfies: (CG b 1) G(x, y, z) = 0 if x = y = z; (CG b 2) 0 ≺ G(x, x, y) for all x, y ∈ X with x ≠ y; (CG b 3) G(x, x, y) ≤ G(x, y, z) for all x, y, z ∈X with y≠z; (CG b 4) G(x, y, z) = G(p{x, y, z}), where p is a permutation of x, y, z;