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

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  • N. Hussain
  • S. Khaleghizadeh
  • P. Salimi
  • F. Akbar

Abstract

We introduce the concept of an -admissible non-self-mappings with respect to and establish the existence of PPF dependent fixed and coincidence point theorems for - -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 -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.

Suggested Citation

  • N. Hussain & S. Khaleghizadeh & P. Salimi & F. Akbar, 2013. "New Fixed Point Results with PPF Dependence in Banach Spaces Endowed with a Graph," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, December.
    • Handle: RePEc:hin:jnlaaa:827205
    DOI: 10.1155/2013/827205
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    Cited by:

    1. Yeol Je Cho & Shin Min Kang & Peyman Salimi, 2018. "Some PPF Dependent Fixed Point Theorems for Generalized α - F -Contractions in Banach Spaces and Applications," Mathematics, MDPI, vol. 6(11), pages 1-19, November.

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