In this paper, an efficient new iterative method for approximating the fixed point of Suzuki mappings is proposed. Some important weak and strong convergence results of the proposed iterative method are established in the setting of Banach space. An example illustrates the theoretical outcome.

We introduce the notion of the C⁎-algebra-valued G-metric space. The existence and uniqueness of some fixed-point theorems for self-mappings with contractive or expansive conditions on complete C⁎-algebra-valued G-metric spaces are proved. As an application, we prove the existence and uniqueness of the solution of a type of differential equations.

In this work, we show that the existence of fixed points ofF-contraction mappings in function weighted metric spaces can be ensured without third condition ( F 3 ) (F3) imposed on Wardowski function F :(0, ∞ ) → ℜ F\mathrm{:(0,\hspace{0.33em}}\infty )\to \Re . The present article investigates (common) fixed points of rational typeF-contractions for single-valued mappings. The article employs Jleli and Samet’s perspective of a new generalization of a metric space, known as a function weighted metric space. The article imposes the contractive condition locally on the closed ball, as well as, globally on the whole space. The study provides two examples in support of the results. The presented theorems reveal some important corollaries. Moreover, the findings further show the usefulness of fixed point theorems in dynamic programming, which is widely used in optimization and computer programming. Thus, the present study extends and generalizes related previous results in the literature in an empirical perspective.

In this article, we introduce the class of enriched Suzuki nonexpansive (ESN) mappings. We show that this new class of mappings properly contains the class of Suzuki nonexpansive as well as the class of enriched nonexpansive mappings. We establish existence of fixed point and convergence of fixed point in a Hilbert space setting under the Krasnoselskii iteration process. One of the our main results is applied to solve a split feasibility problem (SFP) in this new setting of mappings. Our main results are a significant improvement of the corresponding results of the literature.

The main objective of this manuscript is to define the concepts of F-(⋏,h)-contraction and ($\alpha$,$\eta )$-Reich type interpolative contraction in the framework of orthogonal $\mathfrak{F}$-metric space and prove some fixed point results. Our primary result serves as a cornerstone, from which established findings in the literature emerge as natural consequences. To enhance the clarity of our novel contributions, we furnish a significant example that not only strengthens the innovative findings but also facilitates a deeper understanding of the established theory. The concluding section of our work is dedicated to the application of these results in establishing the existence and uniqueness of a solution for a fractional differential equation of anomalous diffusion.