New fixed point results under generalized $c$-distance in $tvs$-cone $b$-metric spaces with an application to systems of Fredholm integral equations

Authors

  • Ghasem Soleimani Rad Young Researchers and Elite club, Central Tehran Branch, Islamic Azad University, Tehran, Iran
  • Kamal Fallahi Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran
  • Zoran Kadelburg University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Beograd, Serbia

DOI:

https://doi.org/10.30495/jme.v12i1.718

Keywords:

$tvs$-cone $b$-metric space, generalized $c$-distance, fixed point, periodic point, system of integral equations

Abstract

In this paper, we define a generalized $c$-distance in $tvs$-cone$b$-metric spaces and introduce some results about its properties.Then we prove some new fixed point and common fixed point results(with the underlying cone which is not normal). Respective resultsconcerning mappings without periodic points are also deduced. Someexamples are presented to validate our obtained results. Anapplication to system of Fredholm integral equations is presented.

Author Biographies

Ghasem Soleimani Rad, Young Researchers and Elite club, Central Tehran Branch, Islamic Azad University, Tehran, Iran

Assistant Professor

Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

Kamal Fallahi, Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

Assistant Professor

Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

Zoran Kadelburg, University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Beograd, Serbia

Professor

University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Beograd, Serbia

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Published

2018-06-29

Issue

Vol. 12

Section

Vol. 12, No. 4, (2018)

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