In this paper we propose a new three-step iteration process, called M iteration process, for approximation of fixed points. Some weak and strong convergence theorems are proved for Suzuki generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Numerical example is given to show the efficiency of new iteration process. Our results are the extension, improvement and generalization of many known results in the literature of iterations in fixed point theory.

In this paper, we initiate the notion of generalized multivalued $({\alpha }_K^{*},\mathsf{{\rm Y}},\mathsf{\Lambda })$ -contractions and provide some new common fixed point results in the class of ${\alpha }_K$ -complete partial b-metric spaces. The obtained results are an improvement of several comparable results in the existing literature. We set up an example to elucidate our main result. Moreover, we present applications dealing with the existence of a solution for systems either of functional equations or of nonlinear matrix equations.

In this paper, we initiate the notion of Ćirić type rational graphic $\left(\mathsf{{\rm Y}},\Lambda \right)$ -contraction pair mappings and provide some new related common fixed point results on partial b-metric spaces endowed with a directed graph G. We also give examples to illustrate our main results. Moreover, we present some applications on electric circuit equations and fractional differential equations.

We prove a result on points of coincidence and common fixed points for three self-mappings satisfying generalized contractive type conditions in cone metric spaces. We deduce some results on common fixed points for two self-mappings satisfying contractive type conditions in cone metric spaces. These results generalize some well-known recent results.

We introduce the notion of cone rectangular metric space and prove Banach contraction mapping principle in cone rectangular metric space setting. Our result extends recent known results.