On some mappings with a unique fixed point

Górnicki, Jarosław

doi:10.1007/s11784-019-0741-8

Cited by 14 publications

(11 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the present paper, we have extended the recent results of Górnicki [21] to their set-valued counterparts. Our main contribution in this paper is the defining two new contractive inequalities for set-valued maps.…”

Section: Discussionmentioning

confidence: 77%

“…Inspired by the work of Górnicki [21], in the present paper we present the set-valued versions of his results. Most of the contractive conditions existing in literature produce fixed points but they force the map under consideration to be continuous as well.…”

Section: Remarkmentioning

confidence: 98%

“…Recently, Górnicki [21] has shown that there are non-linear maps those admit unique fixed point but the maps need not be continuous at the fixed point. He replaced the constant M in condition (1) by control functions.…”

Section: Remarkmentioning

confidence: 99%

“…The recent proofs due to Górnicki [21] will be taken as a framework and his proofs will be extended to their set-valued analogues using the function ∆ and the Pompeiu-Hausdorff metric P H.…”

Section: Geraghty-type Contractive Inequalitymentioning

confidence: 99%

See 3 more Smart Citations

Contractive Inequalities for Some Asymptotically Regular Set-Valued Mappings and Their Fixed Points

Debnath

Sen

2020

Symmetry

View full text Add to dashboard Cite

The symmetry concept is a congenital characteristic of the metric function. In this paper, our primary aim is to study the fixed points of a broad category of set-valued maps which may include discontinuous maps as well. To achieve this objective, we newly extend the notions of orbitally continuous and asymptotically regular mappings in the set-valued context. We introduce two new contractive inequalities one of which is of Geraghty-type and the other is of Boyd and Wong-type. We proved two new existence of fixed point results corresponding to those inequalities.

show abstract

Section: Discussionmentioning

confidence: 77%

Section: Remarkmentioning

confidence: 98%

Section: Remarkmentioning

confidence: 99%

Section: Geraghty-type Contractive Inequalitymentioning

confidence: 99%

See 2 more Smart Citations

Contractive Inequalities for Some Asymptotically Regular Set-Valued Mappings and Their Fixed Points

Debnath

Sen

2020

Symmetry

View full text Add to dashboard Cite

show abstract

“…After then, Bisht [4] refined the result of Górnicki [3] by replacing the continuity condition for the considered mapping with orbitally continuity or p-continuity. Very recently, Górnicki [5] improved these two mentioned results by introducing new contractions, "Geraghty-Kannan type" and "ϕ-Kannan type." He proved the existence of a fixed point for such mappings.…”

Section: Introductionmentioning

confidence: 98%