Fixed point results of an implicit iterative scheme for fractal generations

<abstract><p>In this paper, we derive the escape criteria for general complex polynomial $ f(x) = \sum_{i = 0}^{p}a_{i}x^{i} $ with $ p\geq2 $, where $ a_{i} \in \mathbb{C} $ for $ i = 0, 1, 2, \dots, p $ to generate the fractals. Moreover, we study the orbit of an implicit iteration (i.e., Jungck-Ishikawa iteration with $ s $-convexity) and develop algorithms for Mandelbrot set and Multi-corn or Multi-edge set. Moreover, we draw some complex graphs and observe how the graph of Mandelbrot set and Multi-corn or Multi-edge set vary with the variation of $ a_{i} $'s.</p></abstract>

The modified Ishikawa iteration process with errors in CAT(0) spaces

In this article, Δ-convergence and strong convergence of the modified Ishikawa iteration process with errors are established for continuous mappings of asymptotically nonexpansive type in CAT(0) spaces. Our results extend and improve the previous results given by many authors.

A unifying approach for some nonexpansiveness conditions on modular vector spaces

This paper provides a new, symmetric, nonexpansiveness condition to extend the classical Suzuki mappings. The newly introduced property is proved to be equivalent to condition (E) on Banach spaces, while it leads to an entirely new class of mappings when going to modular vector spaces; anyhow, it still provides an extension for the modular version of condition (C). In connection with the newly defined nonexpansiveness, some necessary and sufficient conditions for the existence of fixed points are stated and proved. They are based on Mann and Ishikawa iteration procedures, convenient uniform convexities and properly selected minimizing sequences.

Approximation of Fixed Points of C*-Algebra-Multi-Valued Contractive Mappings by the Mann and Ishikawa Processes in Convex C*-Algebra-Valued Metric Spaces

The aim of the present paper is to state and prove some convergence theorems for the Mann and Ishikawa iteration schemes involving C * -algebra-multi-valued contractive mappings in the setting of convex C * -algebra-valued metric spaces. The convergence theorems of the proposed iterations to a common fixed point of finite and infinite family of such mappings are also established.

A generalization of the (CN) inequality and its applications

We extend the (CN) inequality of Bruhat and Tits in CAT(0) spaces to the general setting of uniformly convex hyperbolic spaces. We also show that, under some appropriate conditions, the sequence of Ishikawa iteration defined by Panyanak converges to a strict fixed point of a multi-valued Suzuki mapping.

Approximation of endpoints for multivalued nonexpansive mappings in geodesic spaces

Let [Formula: see text] be a complete CAT(0) space, [Formula: see text] be a closed and convex subset of [Formula: see text] and [Formula: see text] be a multivalued nonexpansive mapping. We prove that the sequence of Ishikawa iteration converges to an endpoint of [Formula: see text]. This improves, extends and unifies some recently announced results of the current literature.