Abstract and Applied Analysis

New Fixed Point Results with PPF Dependence in Banach Spaces Endowed with a Graph

N. Hussain, S. Khaleghizadeh, P. Salimi, and F. Akbar

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Abstract

We introduce the concept of an α c -admissible non-self-mappings with respect to η c and establish the existence of PPF dependent fixed and coincidence point theorems for α c η c - ψ -contractive non-self-mappings in the Razumikhin class. As applications of our PPF dependent fixed point and coincidence point theorems, we derive some new fixed and coincidence point results for ψ -contractions whenever the range space is endowed with a graph or with a partial order. The obtained results generalize, extend, and modify some PPF dependent fixed point results in the literature. Several interesting consequences of our theorems are also provided.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 827205, 9 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393443689

Digital Object Identifier
doi:10.1155/2013/827205

Mathematical Reviews number (MathSciNet)
MR3143545

Zentralblatt MATH identifier
07095403

Citation

Hussain, N.; Khaleghizadeh, S.; Salimi, P.; Akbar, F. New Fixed Point Results with PPF Dependence in Banach Spaces Endowed with a Graph. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 827205, 9 pages. doi:10.1155/2013/827205. https://projecteuclid.org/euclid.aaa/1393443689


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