In this manuscript, we prove the existence and uniqueness of a common fixed point for continuous self-mapping over closed subset Hilbert space satisfying non-linear rational type contraction condition.

The current study attempts to identify a new generalized metric space structure, referred as partial modular b−metric, that extends both via b−metric and explains the topological aspects of implementing examples. In addition, contraction mapping modified interpolative almost E−type is determined, which an interpretation bestowed with E−contraction well simulation function fixed point theorem en...

In this paper, we introduce a notion of convex F-contraction and establish some fixed point results for such contractions in b-metric spaces. Moreover, give supportive example to show that our is quite different from the used existing literature since does not necessarily contain continuous mapping but contains mapping. addition, via facts, claim indeed generalize improve previous literature.

The aim of this paper is to propose a new generalization metric space which may open framework. As an application, we consider the analog Banach contraction mapping principle that works properly.

The well-known Banach’s fixed point theorem asserts that ifD X, f is contractive and X, d is complete, then f has a unique fixed point inX. It is well known that the Banach contraction principle 1 is a very useful and classical tool in nonlinear analysis. In 1969, Boyd and Wong 2 introduced the notion ofΦ-contraction. A mapping f : X → X on a metric space is called Φ-contraction if there exists...