Skip to main content
SpringerLink
Log in

A fixed point theorem for a system of Pachpatte operator equations

  • Published:
Aequationes mathematicae Aims and scope Submit manuscript

Abstract

In this paper, we investigate sufficient conditions for the existence of solutions to the system

$$\begin{aligned} \left\{ \begin{array}{l} Tx = x,\\ \alpha _i(x) = 0_E,\quad i=1,2,\ldots ,r , \end{array} \right. \end{aligned}$$

where \(0_E\) is the zero vector of E, and \(\alpha _i :E\rightarrow E \; \; i=1,2,\ldots , r\) are mappings, T is a mapping satisfying the Pachpatte-contraction.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Achari, J.: On Ćirić’s non-unique fixed points. Mat. Vesnik 13, 255–257 (1976)

    MathSciNet  MATH  Google Scholar 

  2. Ćirić, L.B.: On some maps with a non-unique fixed point. Publ. Inst. Math. 17, 52–58 (1974)

    MathSciNet  MATH  Google Scholar 

  3. Ćirić, L.B.: Some Recent Results in Metrical Fixed Point Theory. University of Belgrade, Beograd (2003)

    Google Scholar 

  4. Ćirić, L.B., Jotić, N.: A further extension of maps with non-unique fixed points. Mat. Vesnik 50, 1–4 (1998)

    MathSciNet  MATH  Google Scholar 

  5. Karapınar, E.: Fixed point theorems in cone Banach spaces. Fixed Point Theory Appl. 2009, 609281 (2009). https://doi.org/10.1155/2009/609281

  6. Karapınar, E.: Some nonunique fixed point theorems of ciric type on cone metric spaces. Abstr. Appl. Anal. 2010, 123094 (2010) https://doi.org/10.1155/2010/123094

  7. Karapınar, E.: Couple fixed point theorems for nonlinear contractions in cone metric spaces. Comput. Math. Appl. 59(12), 3656–3668 (2010). https://doi.org/10.1016/j.camwa.2010.03.062

    Article  MathSciNet  MATH  Google Scholar 

  8. Karapınar, E.: A new non-unique fixed point theorem. J. Appl. Funct. Anal. 7(1–2), 92–97 (2012)

    MathSciNet  MATH  Google Scholar 

  9. Pachpatte, B.G.: On Ćirić type maps with a non-unique fixed point. Indian J. Pure Appl. Math. 10(8), 1039–1043 (1979)

    MathSciNet  MATH  Google Scholar 

  10. Rakočević, V., Samet, B.: A fixed point problem under a finite number of equality constraint involving a Ćirić operator. Filomat 31(11), 3193–3202 (2017)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Çankaya University, 06790, Etimesgut, Ankara, Turkey

    Erdal Karapınar

  2. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan

    Erdal Karapınar

  3. Department of Mathematics, Bolu Abant İzzet Baysal University, 14030, Bolu, Turkey

    Ali Öztürk

  4. Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, Niš, 18000, Serbia

    Vladimir Rakočević

Authors
  1. Erdal Karapınar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali Öztürk
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vladimir Rakočević
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir Rakočević.

Ethics declarations

Conflict of interest

The authors declare that they have no competing interests.

Authors’ contribution

All authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Karapınar, E., Öztürk, A. & Rakočević, V. A fixed point theorem for a system of Pachpatte operator equations. Aequat. Math. 95, 245–254 (2021). https://doi.org/10.1007/s00010-020-00724-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00010-020-00724-3

Keywords

Mathematics Subject Classification

Search

Navigation