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Some PPF Dependent Fixed Point Theorems for Generalized α - F -Contractions in Banach Spaces and Applications

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  • Yeol Je Cho

    (Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
    School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Shin Min Kang

    (Department of Mathematics and the RINS, Gyeongsang National University, Jinju 52828, Korea)

  • Peyman Salimi

    (Young Researchers and Elite Club, Rasht Branch, Islamic Azad University, P.O. Box 3516-41335, Rasht, Iran)

Abstract

In this paper, we introduce the concepts of an α -admissible nonself-mapping, an α - F -contractive nonself-mapping, a weak α - F -contractive nonself-mapping, and a generalized α - F -contractive nonself-mapping and prove some P P F (past-present-future)-dependent fixed point theorems for the proposed contractive nonself-mappings in certain Razumikhin classes. By using our results, we derive some P P F -dependent fixed point theorems for an α - F -contractive nonself-mapping endowed with a graph or a partial order. Finally, we give some applications to illustrate the main results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:11:p:267-:d:183898
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    References listed on IDEAS

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    1. Ravi P. Agarwal & Nawab Hussain & Mohamed-Aziz Taoudi, 2012. "Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, July.
    2. Erdal Karapınar & Bessem Samet, 2012. "Generalized 𠜶 - ð Contractive Type Mappings and Related Fixed Point Theorems with Applications," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-17, September.
    3. Marwan Amin Kutbi & Wutiphol Sintunavarat, 2014. "On Sufficient Conditions for the Existence of Past-Present-Future Dependent Fixed Point in the Razumikhin Class and Application," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, February.
    4. N. Hussain & S. Al-Mezel & P. Salimi, 2013. "Fixed Points for -Graphic Contractions with Application to Integral Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, October.
    5. 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.
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