Abstract
We introduce the concept of the generalized -contraction mappings and establish the existence of fixed point theorem for such mappings by using the properties of -distance and -admissible mappings. We also apply our result to coincidence point and common fixed point theorems in metric spaces. Further, the fixed point theorems endowed with an arbitrary binary relation are also derived from our results. Our results generalize the result of Kutbi, 2013, and several results in the literature.
Highlights
It is well known that many problems in many branches of mathematics can be transformed to a fixed point problem of the form Tx = x for self-mapping T defined on framework of metric space (X, d)
We introduce the new mapping, the so-called generalized wα-contraction mapping, and prove the fixed point results for this mapping by using w-distance
We give the notion of wα-contraction mapping and prove the existence of fixed point theorem for such mapping
Summary
Suzuki and Takahashi [15] established the fixed point result for multivalued mapping with respect to w-distance This result is an improvement of the Nadler’s fixed point theorem. Kutbi [20] established useful lemma for w-distance which is an improved version of the lemma given in [21] and proved a key lemma on the existence of f-orbit for generalized f-contraction mappings. He gave the existence of coincidence points and common fixed points for generalized f-contraction mappings not involving the extended Hausdorff metric. Our results improve and complement the main result of Kutbi [20] and many results in the literature
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