Abstract
In this paper, using rational type contractions, common fuzzy fixed point result for Φ contractive mappings involving control functions as coefficients of contractions in the setting of complex-valued metric space is established. The derived results generalizes some result in the existing literature. To show the validity of the derived results an appropriate example and applications are also discussed.
Highlights
Fixed point theory is considered to be the most interesting and dynamic area of research in the development of nonlinear analysis
Banach contraction principal [1] is an initiative for researchers during last few decades
Banach contraction principal has been generalized in different directions by changing the condition of contraction or by the underlying space
Summary
Fixed point theory is considered to be the most interesting and dynamic area of research in the development of nonlinear analysis. Dass and Gupta [9] extended the Banach contraction principal for rational type inequality and obtained fixed point results in metric space, which is further extended to different spaces by many authors. In the researchers realized that where division occurs in cone metric spaces, the concept of rational type contraction is not meaningful To overcome this problem a new metric space was recently established by Azam et al [10], known as complex-valued metric space, where the author obtained fixed point results via rational type contractive condition. In [13, 14], the authors extended common fixed point results for multivalued mappings in complex-valued metric space. Heilpern [16] established the concept of fuzzy mappings and obtained fixed point results in metric linear space.
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