In this paper, we introduce the notion of fuzzy bipolar metric space and prove some fixed point results in this space. We provide some non-trivial examples to support our claim and also give applications for the usability of the main result in fuzzy bipolar metric spaces.
Some fixed point theorems are developed in fuzzy metric spaces using an altering distance function under binary relationship. We ensure the existence and uniqueness of the solution to ordinary differential equation using our results. We also give a non-trivial example to illustrate our primary result. Our results strengthen and extend the Theorem 3.1 of Shen et al. (Applied Mathematics Letters, 25 (2012), 138-141).
In this paper, we introduce a new iteration scheme, named as the S**-iteration scheme, for approximation of fixed point of the nonexpansive mappings. This scheme is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our instigated scheme and give a numerical example to vindicate our claim. We also put forward some weak and strong convergence theorems for Suzuki's generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Our results comprehend, improve, and consolidate many results in the existing literature.
We essentially suggest the concept of mutual sequences and Cauchy mutual sequence and utilize the same to prove the existence and uniqueness of common fixed point results for finite number of self- and non-self-mappings using fuzzy
ℤ
∗
-contractive mappings in fuzzy metric spaces. Our main result was obtained under generalized contractive condition in the fuzzy metric spaces. We provide examples to vindicate the claims and usefulness of such investigations. In this way, the present results generalize and enrich the several existing literature of the fuzzy metric spaces.
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