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Scrutiny of some fixed point results by S-operators without triangular inequality

  • Farshid Khojasteh EMAIL logo and Hassan Khandani
Published/Copyright: March 10, 2020
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 70 Issue 2

Abstract

In this work, the discussion centers on introducing non-triangular metric as a generalization of JS-metric, which may lessen the frantic pace of working on generalizing the triangle inequality by omitting it from the original ordinary metric’s definition. Then, we present S-operators as a new sort of mappings included some properties in order to characterize some known contractions. After that, we graft non-triangular metric onto S-operators in order to make the worthwhile fixed point results facile to prove and conceive.

MSC 2010: Primary 47H10; 37C25
Keywords: 𝓩-contraction; non-triangular metric space; JS-metric space; simulation function; quasi-contraction; S-operator

The first author wishes to thank all the members of the Young Researcher and Elite Club of Islamic Azad University of Arak for completely supported the research cause of wining the Best Scholar Award in Markazi province in Iran at 2019.

Acknowledgement

The first author wishes to thank all the members of the Young Researcher and Elite Club of Islamic Azad University of Arak for completely supported the research cause of wining the Best Scholar Awards in Markazi province in Iran at 2019.

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Received: 2019-05-16
Accepted: 2019-08-19
Published Online: 2020-03-10
Published in Print: 2020-04-28

© 2020 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  1. Regular papers
  2. Relatively residuated lattices and posets
  3. Strongly s-dense injective hull and Banaschewski’s theorems for acts
  4. Wild sets in global function fields
  5. Generators and integral points on elliptic curves associated with simplest quartic fields
  6. New Filbert and Lilbert matrices with asymmetric entries
  7. Returning functions with closed graph are continuous
  8. On sets of points of approximate continuity and ϱ-upper continuity
  9. Investigation of the fifth Hankel determinant for a family of functions with bounded turnings
  10. On solvability of some nonlocal boundary value problems for biharmonic equation
  11. The study of piecewise pseudo almost periodic solutions for impulsive Lasota-Wazewska model with discontinuous coefficients
  12. Strongly increasing solutions of higher-order quasilinear ordinary differential equations
  13. Oscillation of second order half-linear neutral differential equations with weaker restrictions on shifted arguments
  14. Filippov solutions of vector Dirichlet problems
  15. Sequences of positive homoclinic solutions to difference equations with variable exponent
  16. Modified Lupaş-Jain operators
  17. New fixed point results in bv(s)-metric spaces
  18. Improved Young and Heinz operator inequalities for unitarily invariant norms
  19. Scrutiny of some fixed point results by S-operators without triangular inequality
  20. The lattices of families of regular sets in topological spaces
  21. Iterated partial summations applied to finite-support discrete distributions
  22. Hamiltonicity of a class of toroidal graphs
https://doi.org/10.1515/ms-2017-0364
Keywords for this article
𝓩-contraction; non-triangular metric space; JS-metric space; simulation function; quasi-contraction; S-operator

Articles in the same Issue

  1. Regular papers
  2. Relatively residuated lattices and posets
  3. Strongly s-dense injective hull and Banaschewski’s theorems for acts
  4. Wild sets in global function fields
  5. Generators and integral points on elliptic curves associated with simplest quartic fields
  6. New Filbert and Lilbert matrices with asymmetric entries
  7. Returning functions with closed graph are continuous
  8. On sets of points of approximate continuity and ϱ-upper continuity
  9. Investigation of the fifth Hankel determinant for a family of functions with bounded turnings
  10. On solvability of some nonlocal boundary value problems for biharmonic equation
  11. The study of piecewise pseudo almost periodic solutions for impulsive Lasota-Wazewska model with discontinuous coefficients
  12. Strongly increasing solutions of higher-order quasilinear ordinary differential equations
  13. Oscillation of second order half-linear neutral differential equations with weaker restrictions on shifted arguments
  14. Filippov solutions of vector Dirichlet problems
  15. Sequences of positive homoclinic solutions to difference equations with variable exponent
  16. Modified Lupaş-Jain operators
  17. New fixed point results in bv(s)-metric spaces
  18. Improved Young and Heinz operator inequalities for unitarily invariant norms
  19. Scrutiny of some fixed point results by S-operators without triangular inequality
  20. The lattices of families of regular sets in topological spaces
  21. Iterated partial summations applied to finite-support discrete distributions
  22. Hamiltonicity of a class of toroidal graphs
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