Some novel fixed point theorems in partially ordered metric spaces

Vishal Gupta; Gerald Jungck; Naveen Mani; Vishal Gupta; Gerald Jungck; Naveen Mani

doi:10.3934/math.2020284

AIMS Mathematics

2020, Volume 5, Issue 5: 4444-4452. doi: 10.3934/math.2020284

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Research article

Some novel fixed point theorems in partially ordered metric spaces

1.
Department of Mathematics, Maharishi Markandeshwar, Deemed to be University, Mullana, Haryana, India
2.
Department of Mathematics, Bradley University, Peoria- 61625, Illinois, United States
3.
Department of Mathematics, Sandip University, Nashik, Maharashtra, India

Received: 03 December 2019 Accepted: 07 May 2020 Published: 13 May 2020
MSC : 46TXX, 47H10, 54H25

Our aim in this communication is to present a new type of contraction and common fixed point results for non-continuous self mappings without using the compatibility and commutative property. Moreover, we have found common fixed point without using the Cauchy's criterion for convergence. Some illustrative examples with graphical representation and remarks are given to justify that the contraction introduced in the main result is new and unique, which will be useful for future researches.
- fixed point,
- continuity,
- compatibility,
- contraction,
- partially ordered metric spaces
Citation: Vishal Gupta, Gerald Jungck, Naveen Mani. Some novel fixed point theorems in partially ordered metric spaces[J]. AIMS Mathematics, 2020, 5(5): 4444-4452. doi: 10.3934/math.2020284

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Abstract

Our aim in this communication is to present a new type of contraction and common fixed point results for non-continuous self mappings without using the compatibility and commutative property. Moreover, we have found common fixed point without using the Cauchy's criterion for convergence. Some illustrative examples with graphical representation and remarks are given to justify that the contraction introduced in the main result is new and unique, which will be useful for future researches.

References

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