Abstract
In this work, we introduce a generalized fixed point theorem using a complex C-class function as a new tool in complex valued G_{b}-metric spaces. Moreover, we define alpha -(F,psi ,varphi )-contractive type and α-admissible mapping. Then we prove a fixed point theorem using these notions and the complex C-class function. The obtained results generalize some facts in the literature.
Highlights
Fixed point theory has great importance in science and mathematics
Let us define the α – (F, ψ, φ)-contractive self-mapping as a new concept in complex valued Gb-metric space
4 Conclusions We have introduced a generalized fixed point theorem using the complex C-class function as a new tool in complex valued Gb-metric spaces
Summary
Fixed point theory has great importance in science and mathematics. Since this area has been developed very fast over the past two decades due to huge applications in various fields such as nonlinear analysis, topology and engineering problems, it has attracted considerable attention from researchers.In 1989, Bakhtin [1] presented b-metric spaces. After introducing the α – (F, ψ, φ)-contractive type and α-admissible mapping and complex C-class function, we give the proof of a new fixed point theorem. Definition 2.2 ([17]) Let {xn} be a sequence in a complex valued Gb-metric space (X, G).
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