This paper establishes new fixed point theorems based on the concept of F-contractions. The results are formulated for multivalued mappings of rational type defined on spherically complete ultrametric spaces. Several special cases are discussed, some of which generalize or improve upon known results. Illustrative examples are provided to support the theoretical findings. Furthermore, an alternative generalization involving almost contractive multivalued mappings of rational type is also presented within the framework of F-contractions.
This study presents a comparison of various inverse soft covering upper approximations, focusing specifically on the differences between them. A key finding of our work is the introduction of a new type of inverse soft covering upper approximation which is a new approach in developing inverse soft covering based rough sets. We demonstrate that this new approximation is smaller than the three existing approximations described in the literature. Based on this result, we aim to manage the decision-making processes, especially for the uncertainty problems, in a more ideal way.
In this paper, we introduce the notion of semi uniform alpha convergence for sequences of functions between metric spaces. We also provide some results concerning the relationship between uniform exhaustiveness, semi uniform exhaustiveness and semi uniform alpha convergence. Finally, we give a Korovkin-type theorem related to uniform exhaustiveness.
This research presents a comprehensive theoretical and computational analysis of the Kirk order-2 iteration method for approximating fixed points of operators that satisfy a weak contractive condition within the framework of a real Banach space. The primary objectives are to establish the strong convergence, stability, and computational efficiency of this iterative scheme. A key contribution of this work is a detailed self-comparative analysis of the convergence rate among six distinct permutations of the iterative scheme's coefficients. We derive a precise analytical condition that determines which permutation yields a faster convergence rate, providing a theoretical framework for optimizing the algorithm's performance. Numerical results are presented to validate the theoretical findings and demonstrate the algorithm's efficiency, confirming that specific permutations of the coefficients can significantly accelerate convergence.
We give some new embeddings results for weighted grand Lebesgue spaces L-omega(p)),delta (Omega), where Omega subset of R-d is a open bounded subset. We also obtain the boundedness of the Kantorovich operator K-n in L-omega(p),delta) [0, 1]. In addition, we establish two direct estimates by K-functionals of the rate of approximation in L-omega(p),delta) [0,1].We generalize the direct estimate inequality in classical Lebesgue spaces L-p [0,1] to L-omega(p),delta)[0,1] using the boundedness of the Hardy-Littlewood maximal operator in L-omega(p),delta) [0,1]. Finally, we obtain similar results in [8] for the spaces L-omega(p),delta) [0,1].
