Common fixed point theorems under a new continuity condition

Pant, Neeraj; Bisht, Ravindra K.

doi:10.1007/s11565-011-0141-5

Cited by 35 publications

(39 citation statements)

References 17 publications

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“…Here, some common fixed point theorems in diverse settings were obtained as an application of the new notion introduced. Of particular importance is the following result from Pant and Bisht [10].…”

Section: And T If T(x) = X = S(x)mentioning

confidence: 97%

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Extension of Some Common Fixed Point Theorems

Patel¹,

Deheri²

2013

IJAPM

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Abstract-It is well-known that the classical Banach's fixed point theorem has been generalized in various directions. This celebrated result has been extended to the theory of common fixed points. A few theorems dealing with the existence and uniqueness of common fixed points are presented here. These results not only extend but also sharpens some of the well known results found in the literature. There is a result which says that there does exist an improvement in the rate of convergence also.Index Terms-Banach fixed point theorem, common fixed point, hilbert space, uniqueness.

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Section: And T If T(x) = X = S(x)mentioning

confidence: 97%

“…Recently, Pant and Bisht [10] unified the approaches of reciprocal continuity, subsequential continuity and conditional commutativity to generalize the notion of reciprocal continuity. Here, some common fixed point theorems in diverse settings were obtained as an application of the new notion introduced.…”

Section: And T If T(x) = X = S(x)mentioning

confidence: 99%

Extension of Some Common Fixed Point Theorems

Patel¹,

Deheri²

2013

IJAPM

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“…Jungck [10] introduced the concept of compatibility for a pair of self maps, which has been extended to hybrid pair of maps by Kaneko and Sessa [15] and Beg and Azam [5] when T : X → CB(X). Recently, Bouhadjera and Godet Tobie [7] introduced subsequential continuity which is weaker than the reciprocal continuity introduced by pant [19]. In fact every non-vacuously pair of reciprocally continuous maps is naturally subsequentially continuous.…”

Section: Introductionmentioning

confidence: 99%

A coincidence and common fixed point theorem for subsequentially continuous hybrid pairs of maps satisfying an implicit relation

Beloul¹,

Tomar²

2017

Math Morav

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“…In the sequel, it is worthwhile to note that Pant and Bisht [9] introduced the notion of reciprocal continuity and as an application of this concept obtained the first result that established a situation in which a collection of mapping has a fixed point which is a point of discontinuity for all the mappings.…”

Section: Introductionmentioning

confidence: 99%

Weak Reciprocal Continuity and Common Fixed Point Theorems

Patel¹,

Deheri²

2014

IJAPM

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Abstract-This investigation aims to establish the importance of weak reciprocal continuity of the maps in deriving the common fixed point theorems. The existence and uniqueness of the common fixed points are obtained under generalized contractive conditions in the setting of complete metric spaces. That the rate of convergence is duly addressed is manifest in the proofs.Index Terms-Complete metric space, fixed point, weak reciprocal continuity, compatibility.

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Common fixed point theorems under a new continuity condition

Cited by 35 publications

References 17 publications

Extension of Some Common Fixed Point Theorems

Extension of Some Common Fixed Point Theorems

A coincidence and common fixed point theorem for subsequentially continuous hybrid pairs of maps satisfying an implicit relation

Weak Reciprocal Continuity and Common Fixed Point Theorems

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