Some Common Fixed Point Theorems in Generalized Metric Spaces

Kumar, Manoj; Kumar, P. Senthil; Kumar, Sanjay

doi:10.1155/2013/719324

Cited by 8 publications

(5 citation statements)

References 5 publications

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“…Since then, a number of fixed point theorems have been established by several researchers in different settings under common limit range property. For detail description, we refer the reader to [8,32,35,36,43,66].…”

Section: Turns Into D(t X T Y) ≤ ψ(D(x Y))mentioning

confidence: 99%

Fixed Points of Weakly Compatible Mappings Satisfying Generalized $$\varphi $$ φ -Weak Contractions

Vetro

Chauhan²,

Karapınar

et al. 2014

Bull. Malays. Math. Sci. Soc.

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In this paper, utilizing the notion of the common limit range property, we prove some new integral type common fixed point theorems for weakly compatible mappings satisfying a ϕ-weak contractive condition in metric spaces. Moreover, we extend our results to four finite families of self mappings, and furnish an illustrative example and an application to support our main theorem. Our results improve, extend, and generalize well-known results on the topic in the literature. KeywordsMetric space • Weakly compatible mappings • (C L R S ) property • (C L R ST ) property • Fixed point Mathematics Subject Classification 47H09 • 47H10 • 54H25 • 46T99 Communicated by Poom Kumam.

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Section: Turns Into D(t X T Y) ≤ ψ(D(x Y))mentioning

confidence: 99%

Fixed Points of Weakly Compatible Mappings Satisfying Generalized $$\varphi $$ φ -Weak Contractions

Vetro

Chauhan²,

Karapınar

et al. 2014

Bull. Malays. Math. Sci. Soc.

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“…Some of the interesting works for (CLR) property can be cited in [3,4,6,7,[9][10][11]. In a similar mode, we use these properties in complex valued metric spaces.…”

Section: Introductionmentioning

confidence: 99%

Weakly compatible maps in complex valued metric spaces and an application to solve Urysohn integral equation

Kumar

et al. 2016

Filomat

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In this paper, we prove common fixed point theorems for a pair of mappings satisfying rational inequality. Also, we prove common fixed point theorems for weakly compatible maps, weakly compatible along with (CLR) and E.A. properties that generalizes the results of Sintunavarat et al. [15]. Further, we apply our results to find the solution of Urysohn integral equationsb a K 1 (t, s, x(s))ds + (t), x(t) = b a K 2 (t, s, x(s))ds + h(t), where t ∈ [a, b] ⊆ R, x, , h ∈ X and K 1 , K 2 : [a, b] × [a, b] × R n → R n .

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“…Using the (CLR) property and (E.A) property fixed point theorems have been proved by various researchers (see [5]- [10], [12], [15], [16], [17], [20]).…”

Section: Introductionmentioning

confidence: 99%

COMMON FIXED POINT THEOREMS FOR SIX SELF-MAPS SATISFYING COMMON(E.A) AND COMMON(CLR) PROPERTIES IN COMPLEX VALUED METRIC SPACE Vol. 3(1) Jan 2015, No. 23, pp. 228-244 MUHAMMAD SARWAR AND MIAN BAHADUR ZADA

2015

Electronic Journal of Mathematical Analysis and Applications

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Some Common Fixed Point Theorems in Generalized Metric Spaces

Cited by 8 publications

References 5 publications

Fixed Points of Weakly Compatible Mappings Satisfying Generalized $$\varphi $$ φ -Weak Contractions

Fixed Points of Weakly Compatible Mappings Satisfying Generalized $$\varphi $$ φ -Weak Contractions

Weakly compatible maps in complex valued metric spaces and an application to solve Urysohn integral equation

COMMON FIXED POINT THEOREMS FOR SIX SELF-MAPS SATISFYING COMMON(E.A) AND COMMON(CLR) PROPERTIES IN COMPLEX VALUED METRIC SPACE Vol. 3(1) Jan 2015, No. 23, pp. 228-244 MUHAMMAD SARWAR AND MIAN BAHADUR ZADA

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