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KW-Type Nonlinear Contractions and Their Best Proximity Points
Numerical Functional Analysis and Optimization ( IF 1.4 ) Pub Date : 2021-06-03 , DOI: 10.1080/01630563.2021.1933526
Ishak Altun 1 , Mustafa Aslantas 2 , Hakan Sahin 3
Affiliation  

Abstract

In this paper, we present two main results about best proximity points for multivalued mappings. First, taking into account Klim and Wardowski’s approach in fixed-point theory, we obtain a new result for multivalued mappings which includes the main theorem of Kamran [Kamranm, T. (2009). Mizoguchi–Takahashi’s type fixed point theorem. Comput. Math. Appl. 57(3):507–511]. Second, combining this approach with cyclic contraction, we give a general best proximity point result, and so we obtain many well-known fixed-point theorems such as Mizoguchi–Takahashi, Feng–Liu and Klim–Wardowski [Mizoguchi, N., Takahashi, W. (1989). Fixed point theorems for multivalued mappings on complete metric spaces. J. Math. Anal. Appl. 141(1):177–188; Feng, Y., Liu, S. (2006). Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings. J. Math. Anal. Appl. 317(1):103–112; Klim, D., Wardowski, D. (2007). Fixed point theorems for set-valued contractions in complete metric spaces. J. Math. Anal. Appl. 334(1):132–139]. Also, we support our results by providing some nontrivial, illustrative and comparative examples.



中文翻译:

KW 型非线性收缩及其最佳邻近点

摘要

在本文中,我们提出了关于多值映射的最佳邻近点的两个主要结果。首先,考虑到 Klim 和 Wardowski 在不动点理论中的方法,我们获得了多值映射的新结果,其中包括 Kamran [Kamranm, T. (2009) 的主要定理。Mizoguchi-Takahashi 类型不动点定理。计算。数学。应用程序 57(3):507-511]。其次,将此方法与循环收缩相结合,我们给出了一般的最佳邻近点结果,因此我们获得了许多著名的不动点定理,例如 Mizoguchi-Takahashi、Feng-Liu 和 Klim-Wardowski [Mizoguchi, N., Takahashi , W. (1989)。完全度量空间上多值映射的不动点定理。J. 数学。肛门。应用程序 141(1):177-188;Feng, Y., Liu, S. (2006)。多值收缩映射和多值 Caristi 类型映射的不动点定理。J. 数学。肛门。应用程序 317(1):103-112;Klim, D., Wardowski, D. (2007)。完全度量空间中集合值收缩的不动点定理。J. 数学。肛门。应用程序 334(1):132-139]。此外,我们通过提供一些重要的、说明性的和比较的例子来支持我们的结果。

更新日期:2021-07-13
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