A generalized Suzuki Berinde contraction that characterizes Banach spaces

New coincidence point and fixed point theorems for essential distances and $e^{0}$-metrics

In this paper, we establish some new fixed point theorems and coincidence point theorems for essential distances and $e^{0}$-metrics which generalize and improve Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, Nadler's fixed point theorem and Banach contraction principle and many known results in the literature.

Approximating fixed points of enriched Chatterjea contractions by Krasnoselskij iterative method in Banach spaces

Using the technique of enrichment of contractive type mappings by Krasnoselskij averaging, introduced in [Berinde, V., {\it Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces}, Carpathian J. Math. {\bf 35} (2019), no. 3, 277-288.], we introduce the class of enriched Chatterjea contractions and prove general fixed point theorems for such contractions in the setting of a Banach space. Examples to illustrate the richness of the new class of contractions and the relationship between enriched Banach contractions, enriched Kannan contractions an…

On the Suzuki nonexpansive-type mappings

It is shown that if $C$ is a nonempty convex and weakly compact subset of a Banach space $X$ with $M(X)>1$ and $T:C\rightarrow C$ satisfies condition $(C)$ or is continuous and satisfies condition $(C_λ)$ for some $λ\in (0,1)$, then $T$ has a fixed point. In particular, our theorem holds for uniformly nonsquare Banach spaces. A similar statement is proved for nearly uniformly noncreasy spaces.

On some enriched contractions in Banach spaces

In this paper, we introduce two new types of enriched contractions, viz., enriched $\mathcal{A}$-contraction and enriched $\mathcal{A}'$-contraction. Then we obtain fixed points of mappings satisfying such contractions using the fixed point property of the average operator of the mappings. Further, we study the well-posedness and limit shadowing property of the fixed point problem involving the contractions, and give some examples to validate the results proved. We frame an open question related to the existence of a fixed point of such contractions. We also show that Berinde and Păcurar's rec…

Banach 代数中指数和与广义 Lie-Trotter 公式的 Suzuki 型估计

Suzuki Type Estimates for Exponentiated Sums and Generalized Lie-Trotter Formulas in Banach Algebras

本文在 Banach 代数中利用 Jordan 乘积建立 Lie-Trotter 乘积公式的两类误差估计，提出两种广义公式及显式界，并由此直接导出 Suzuki 对称化指数和近似。

Fixed Point Approximation of Suzuki Generalized Nonexpansive Mappings via New Faster Iteration Process

In this paper we propose a new iteration process, called the K iteration process, for approximation of fixed points. We show that our iteration process is faster than the existing leading iteration processes like Picard-S iteration process, Thakur New iteration process and Vatan Twostep iteration process for contraction mappings. We support our analytic proof by a numerical example. Stability of K iteration process and data dependence result for contraction mappings by employing K iteration process is also discussed. Finally we prove some weak and strong convergence theorems for the Suzuki gen…