Fixed point theorems for Kannan type mappings

Górnicki, Jarosław

doi:10.1007/s11784-017-0402-8

Cited by 53 publications

(38 citation statements)

References 10 publications

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“…Recently, J. Górinicki [5] raised the following open question: Question: Does there exists a complete but noncompact metric space (X, d) and a continuous mapping T : X → X such that…”

Section: Resultsmentioning

confidence: 99%

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On Kannan-Type Contractive Mappings

Garai

Dey

Senapati

2018

Numerical Functional Analysis and Optimization

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In this article, we consider Kannan type contractive self-map T on a metric space (X, d) such thatand establish some new fixed point results without taking the compactness of X and also without assuming continuity of T . Further, we anticipate a result ensuring the completeness of the space X via FPP of this map. Finally, we are able to give an affirmative answer to the open question posed by J. Górnicki [Fixed point theorems for Kannan type mappings, J. Fixed Point Theory Appl. 2017]. Apart from these, our manuscript consists of several non-trivial examples which signify the motivation of our investigations.2010 Mathematics Subject Classification. 47H10, 54H25.

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“…Recently, J. Górinicki [5] raised the following open question: Question: Does there exists a complete but noncompact metric space (X, d) and a continuous mapping T : X → X such that…”

Section: Resultsmentioning

confidence: 99%

“…[5] Let (X, d) be a compact metric space and T : X → X be a continuous mapping satisfyingd(T x, T y) < 1 2 {d(x, T x) + d(y, T y)}…”

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confidence: 99%

On Kannan-Type Contractive Mappings

Garai

Dey

Senapati

2018

Numerical Functional Analysis and Optimization

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“…However there are a number of contractive conditions which cannot guarantee the continuity of the mappings, although in most of the cases the continuity of the mapping is assumed. One example of such type of contractive condition is the Kannan type contractive condition and others (see [9]).…”

Section: Introductionmentioning

confidence: 99%

On contractive mappings and discontinuity at fixed points

Garai

Dey

2020

APPL ANAL DISCRETE M

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This paper deals with an interesting open problem of B.E. Rhoades (Contemporary Math. (Amer. Math. Soc.) 72(1988), 233-245) on the existence of general contractive conditions which have fixed points, but are not necessarily continuous at the fixed points. We propose some more solutions to this problem by introducing two new types of contractive mappings, that is, A-contractive and A -contractive, which are, in some sense, more appropriate than those of the important previous attempts. We establish some new fixed point results involving these two contractive mappings in compact metric spaces and also in complete metric spaces and show that these contractive mappings are not necessarily continuous at their fixed points. Finally, we suggest an applicable area, where our main results may be employed.

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“…Kannan type inequalities are different from Banach's contraction inequality and has very different properties including the possibility that the mappings satisfying these inequalities may be discontinuous. These inequalities first appeared in the work of Kannan [21,22] and has been discussed in a large number of subsequent works [10,14,16,19,23].…”

Section: Introductionmentioning

confidence: 99%

Simultaneous Determination of Distance Between Sets by Multivalued Kannan Type Coupling

Choudhury¹,

Maity²,

Metiya³

et al. 2018

ijaa

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In this paper we define a multivalued Kannan type coupling between two subsets of a metric space and use it to obtain the distance between the two subsets through the determination of two pairs of points simultaneously. The problem is a multivalued coupled proximity point problem which falls under the general category of global optimization and is approached from the standpoint of fixed point theory. We use UC-property which is a geometric property that holds automatically for appropriate pairs of subsets of uniformly convex Banach spaces and is adapted to metric spaces by certain postulations. The main results are illustrated with examples. Corresponding results are obtained in Banach spaces. The work is in the domain of setvalued analysis.

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Fixed point theorems for Kannan type mappings

Cited by 53 publications

References 10 publications

On Kannan-Type Contractive Mappings

On Kannan-Type Contractive Mappings

On contractive mappings and discontinuity at fixed points

Simultaneous Determination of Distance Between Sets by Multivalued Kannan Type Coupling

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