Abstract
In this paper, we establish the new concept of rational coupled fuzzy cone contraction mapping in fuzzy cone metric spaces and prove some unique rational-type coupled fixed-point theorems in the framework of fuzzy cone metric spaces by using “the triangular property of fuzzy cone metric.” To ensure the existence of our results, we present some illustrative unique coupled fixed-point examples. Furthermore, we present an application of a Lebesgue integral-type contraction mapping in fuzzy cone metric spaces and to prove a unique coupled fixed-point theorem.
Highlights
In 1965, the theory of fuzzy sets was introduced by Zadeh [1]
Oner et al [26] introduced the concept of fuzzy cone metric space (FCMS) and proved a “fuzzy cone Banach contraction theorem” for fixed point (FP) in complete FCMSs in which they assumed that the “fuzzy cone contractive sequences are Cauchy.”
We shall study some unique coupled FP results in FCMSs under the rational coupled fc − contraction conditions with examples
Summary
In 1965, the theory of fuzzy sets was introduced by Zadeh [1]. Kramosil and Michalek [2] introduced the notion of FMS by using continuous t-norm with fuzzy sets. The rational-type fuzzy contraction concept in FMS is given by Rehman et al [13], and they proved some FP results with an application. Oner et al [26] introduced the concept of fuzzy cone metric space (FCMS) and proved a “fuzzy cone Banach contraction theorem” for FP in complete FCMSs in which they assumed that the “fuzzy cone contractive (fc − contractive) sequences are Cauchy.”.
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