Toward a generalized contractive condition in partial metric spaces with the existence results of fixed points and best proximity points

Fixed point theorems for mappings satisfying Geraghty-type contractive conditions are proved in the frame of partial metric spaces, ordered partial metric spaces, and metric-type spaces. Examples are given showing that these results are proper extensions of the existing ones.

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Fixed point theorems for expansive mappings in Gp-metric spaces

Creative Mathematics and Informatics ◽

10.37193/cmi.2017.03.07 ◽

2017 ◽

Vol 26 (3) ◽

pp. 297-308

Author(s):

MELTEM KAYA ◽

◽

HASAN FURKAN ◽

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Common Fixed Point ◽

Metric Space ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Partial Metric ◽

Expansive Mapping ◽

Partial Metric Spaces ◽

Weak Compatibility

In the present paper, we adopt the concept of expansive mapping in the context of Gp-metric spaces in a similar manner expansive mapping in metric spaces. Furthermore, we obtain some results on fixed points of expansive type mappings. Also, we prove some common fixed point results for expansive mappings by using the notion of weak compatibility in Gp-metric space. Our results generalize some comparable results in metric spaces and partial metric spaces to Gp-metric spaces. Moreover, some examples are introduced in order to support our new results.

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FIXED POINTS FOR TWO PAIRS OF ABSORBING MAPPINGS IN WEAK PARTIAL METRIC SPACES

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi2002283p ◽

2020 ◽

pp. 283

Author(s):

Valeriu Popa ◽

Alina-Mihaela Patriciu

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Fixed Points ◽

Point Theorem ◽

Metric Space ◽

Metric Spaces ◽

Partial Metric Space ◽

Partial Metric ◽

Partial Metric Spaces

In this paper, a general fixed point theorem for two pairs of absorbing mappings in weak partial metric space, using implicit relations, has been proved.

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Fixed point results for mappings satisfying (ψ φ)-weakly contractive condition in ordered partial metric spaces

Mathematica Slovaca ◽

10.2478/s12175-013-0141-2 ◽

2013 ◽

Vol 63 (4) ◽

Cited By ~ 1

Author(s):

Hemant Nashine

Keyword(s):

Fixed Point ◽

Metric Spaces ◽

Fixed Point Theory ◽

Point Theory ◽

Contractive Condition ◽

Partial Metric ◽

New Class ◽

Weakly Contractive Condition ◽

Partial Metric Spaces ◽

Weakly Contractive

AbstractIn [18], Matthews introduced a new class of metric spaces, that is, the concept of partial metric spaces, or equivalently, weightable quasi-metrics, are investigated to generalize metric spaces (X, d), to develop and to introduce a new fixed point theory. In partial metric spaces, the self-distance for any point need not be equal to zero. In this paper, we study some results for single map satisfying (ψ,φ)-weakly contractive condition in partial metric spaces endowed with partial order. An example is given to support the useability of our results.

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Fixed Points for Weakα-ψ-Contractions in Partial Metric Spaces

Abstract and Applied Analysis ◽

10.1155/2013/986028 ◽

2013 ◽

Vol 2013 ◽

pp. 1-9 ◽

Cited By ~ 9

Author(s):

Poom Kumam ◽

Calogero Vetro ◽

Francesca Vetro

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Metric Spaces ◽

Partial Metric ◽

Complete Metric Spaces ◽

Contractive Mappings ◽

Partial Metric Spaces

Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weakα-ψ-contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.

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