In this paper, we introduce a generalized multivalued (
α
, L)-almost contraction in the
b
-metric space. Furthermore, we prove the existence and uniqueness of the fixed point for a specific mapping. The result presented in this paper extends some of the earlier results in the existing literature. Moreover, some examples are given to illuminate the usability of the obtained results.
In this manuscript, a class of generalized
ψ
,
α
,
β
-weak contraction is introduced and some fixed point theorems in the framework of
b
-metric space are proved. The result presented in this paper generalizes some of the earlier results in the existing literature. Further, some examples and an application are provided to illustrate our main result.
<abstract><p>This paper reports a modified F-iterative process for finding the fixed points of three generalized $ \alpha $-nonexpansive mappings. We assume certain assumptions to establish the weak and strong convergence of the scheme in the context of a Banach space. We suggest a numerical example of generalized $ \alpha $-nonexpansive mappings which exceeds, properly, the category of functions furnished with a condition (C). After that, we show that our modified F-iterative scheme of this example converges to a common fixed point of three generalized $ \alpha $-nonexpansive mappings. As an application of our main findings, we suggest a new projection-type iterative scheme to solve variational inequality problems in the setting of generalized $ \alpha $-nonexpansive mappings. The main finding of the paper is new and extends many known results of the literature.</p></abstract>
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