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Fixed Points for a Pair of F -Dominated Contractive Mappings in Rectangular b -Metric Spaces with Graph

Author

Listed:
  • Tahair Rasham

    (Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad 44000, Pakistan)

  • Giuseppe Marino

    (Dipartimento di Matematica e Informatica, Universita della Calabria, 87036 Arcavacata di Rende (CS), Italy)

  • Abdullah Shoaib

    (Department of Mathematics and Statistics, Riphah International University, Islamabad 44000, Pakistan)

Abstract

Recently, George et al. (in Georgea, R.; Radenovicb, S.; Reshmac, K.P.; Shuklad, S. Rectangular b-metric space and contraction principles. J. Nonlinear Sci. Appl. 2015, 8, 1005–1013) furnished the notion of rectangular b-metric pace (RBMS) by taking the place of the binary sum of triangular inequality in the definition of a b-metric space ternary sum and proved some results for Banach and Kannan contractions in such space. In this paper, we achieved fixed-point results for a pair of F -dominated mappings fulfilling a generalized rational F -dominated contractive condition in the better framework of complete rectangular b -metric spaces complete rectangular b -metric spaces. Some new fixed-point results with graphic contractions for a pair of graph-dominated mappings on rectangular b -metric space have been obtained. Some examples are given to illustrate our conclusions. New results in ordered spaces, partial b -metric space, dislocated metric space, dislocated b -metric space, partial metric space, b -metric space, rectangular metric spaces, and metric space can be obtained as corollaries of our results.

Suggested Citation

  • Tahair Rasham & Giuseppe Marino & Abdullah Shoaib, 2019. "Fixed Points for a Pair of F -Dominated Contractive Mappings in Rectangular b -Metric Spaces with Graph," Mathematics, MDPI, vol. 7(10), pages 1-9, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:884-:d:269889
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    References listed on IDEAS

    as
    1. 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.
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