Some Random Fixed-Point Theorems for Weakly Contractive Random Operators in a Separable Banach Space

The aim of this paper is to prove a common random fixed-point and some random fixed-point theorems for random weakly contractive operators in separable Banach spaces. A random Mann iterative process is introduced to approximate the fixed point. Finally, the main result is supported by an example and used to prove the existence and the uniqueness of a solution of a nonlinear stochastic integral equation system.

Some New Results of Interpolative Hardy–Rogers and Ćirić–Reich–Rus Type Contraction

In this paper, we present new concepts on completeness of Hardy–Rogers type contraction mappings in metric space to prove the existence of fixed points. Furthermore, we introduce the concept of g -interpolative Hardy–Rogers type contractions in b -metric spaces to prove the existence of the coincidence point. Lastly, we add a third concept, interpolative weakly contractive mapping type, Ćirić–Reich–Rus, to show the existence of fixed points. These results are a generalization of previous results, which we have reinforced with examples.

On Some Common Fixed Point Results for Weakly Contraction Mappings with Application

In this paper, we introduce a new class of generalized weakly contractive mappings and prove common fixed point results by using different algorithms involving this new class of mappings in the framework of b -metric spaces, which generalize the results of Cho. We also provide two examples to show the applicability and validity of our results. As an application of our result, we obtain a solution to an integral equation. Our results extend and improve several comparable results in the existing literature.

Related Fixed Point Theorems in Partially Ordered b -Metric Spaces and Applications to Integral Equations

In this research paper, we have set some related fixed point results for generalized weakly contractive mappings defined in partially ordered complete b -metric spaces. Our results are an extension of previous authors who have already worked on fixed point theory in b -metric spaces. We state some examples and one sample of the application of the obtained results in integral equations, which support our results.

Remarks of Fixed Point for ( ψ , φ )-Weakly Contractive Mappings

In this paper, we obtain a new fixed point theorem for weak contraction mappings on complete generalized metric spaces. Our result is different from that of ( ψ , φ )-weakly contractive mappings which had been obtained by Lakzian–Samet’s [Appl. Math. Lett. 25 (2012) 902–906]. Moreover, an example is given to illustrate the usability of the obtained result.

Common Fixed-Point Theorems of Generalized ψ , φ − Weakly Contractive Mappings in b − Metric-Like Spaces and Application

In this paper, we prove some common fixed-point theorems of generalized ψ , φ − weakly contractive mappings in b − metric-like spaces. We also give two examples to support our results. Meanwhile, we present an application to the existence of solutions for a system of integral equations by means of our results.