New fixed point theorems for orthogonal $F_m$-contractions in incomplete $m$-metric spaces

  • M. Mehmood Riphah International University, Islamabad-44000, Pakistan; University of Wah, Wah Cantt 47040, Pakistan
  • H. Isik Bandırma Onyedi Eylül University, 10200 Bandırma, Balıkesir, Turkey
  • F. Uddin International Islamic University, Islamabad, Pakistan; NUIST Reading Academy, 219 Ningliu Road, Nanjing, Jiangsu, 210044 China
  • A. Shoaib Riphah International University, Islamabad-44000, Pakistan
Keywords: unique fixed point, orthogonal, complete, $\bot_{F_m}$-contraction, incomplete $m$-metric space
Published online: 2021-08-29


In this paper, we introduce the concept of orthogonal $m$-metric spaces and by using $F_m$-contraction in orthogonal $m$-metric spaces, we give the concept of orthogonal $F_m$-contraction (briefly, $\bot_{F_m}$-contraction) and investigate fixed point results for such mappings. Many existing results in the literature appear to be special case of results proved in this paper. An example to support our main results is also mentioned.

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How to Cite
Mehmood M., Isik H., Uddin F., Shoaib A. New Fixed Point Theorems for Orthogonal $F_m$-Contractions in Incomplete $m$-Metric Spaces. Carpathian Math. Publ. 2021, 13 (2), 405-412.