## Abstract and Applied Analysis

### On Best Proximity Point Theorems and Fixed Point Theorems for $p$-Cyclic Hybrid Self-Mappings in Banach Spaces

M. De la Sen

#### Abstract

This paper relies on the study of fixed points and best proximity points of a class of so-called generalized point-dependent $(K,\lambda )$-hybrid $p$-cyclic self-mappings relative to a Bregman distance ${D}_{f}$, associated with a Gâteaux differentiable proper strictly convex function $f$ in a smooth Banach space, where the real functions $\lambda$ and $K$ quantify the point-to-point hybrid and nonexpansive (or contractive) characteristics of the Bregman distance for points associated with the iterations through the cyclic self-mapping. Weak convergence results to weak cluster points are obtained for certain average sequences constructed with the iterates of the cyclic hybrid self-mappings.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 183174, 14 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393444397

Digital Object Identifier
doi:10.1155/2013/183174

Mathematical Reviews number (MathSciNet)
MR3045070

Zentralblatt MATH identifier
1273.47089

#### Citation

De la Sen, M. On Best Proximity Point Theorems and Fixed Point Theorems for $p$ -Cyclic Hybrid Self-Mappings in Banach Spaces. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 183174, 14 pages. doi:10.1155/2013/183174. https://projecteuclid.org/euclid.aaa/1393444397

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