Distance in cone metric spaces and common fixed point theorems

Wang, Shenghua; Guo, Baohua

doi:10.1016/j.aml.2011.04.031

Cited by 35 publications

(41 citation statements)

References 15 publications

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“…Thus all hypotheses of our Theorem 9 are satisfied and z = 0 is a fixed point of T. Note that the mapping T : X X satisfies the condition (2.1) in the main Theorem 2.2 of Wang and Guo [14] with g(x) = x and a 1 = 1/2, a 2 = a 3 = a 4 = 0, but Theorem 2.2 cannot be applied since a cone P is not normed.…”

Section: Fixed Point Theorems For W-cone Distance Contraction Mappingmentioning

confidence: 90%

“…■ Now we shall present an example where our Theorem 9 can be applied, but the main Theorem 2.2 of Wang and Guo [14] cannot.…”

Section: Fixed Point Theorems For W-cone Distance Contraction Mappingmentioning

confidence: 99%

“…Wang and Guo [14]defined the concept of c-distance on a cone metric space in the sense of Huang and Zhang [1], which is also a generalization of w-distance of Kada et al [3]. They proved a common fixed point theorem (Theorem 2.2) by using c-distance in a cone metric space (X, d), where a cone P is normal with normal constant K. Now we shall present an example (Example 7 below), which shows that there are cone metric spaces where underlying cone is not normed, and so theorems of Wang and Guo [14]cannot be applied. On the other case, our presented fixed point theorems for mappings under contractive conditions expressed in the terms of w-distance can be applied, although the underlying cone is not normed.…”

Section: Introductionmentioning

confidence: 99%

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Fixed point theorems for w-cone distance contraction mappings in tvs-cone metric spaces

Ćirić

Lakzian

Rakočević

2012

Fixed Point Theory Appl

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In this article, we introduce the concept of a w-cone distance on topological vector space (tvs)-cone metric spaces and prove various fixed point theorems for w-cone distance contraction mappings in tvs-cone metric spaces. The techniques of the proof of our theorems are more complex then in the corresponding previously published articles, since a new technique was necessary for the considered class of mappings. Presented fixed point theorems generalize results of Suzuki and Takahashi, Abbas and Rhoades, Pathak and Shahzad, Raja and Veazpour, Hicks and Rhoades and several other results existing in the literature. Mathematics subject classification (2010): 47H10; 54H25.

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Section: Fixed Point Theorems For W-cone Distance Contraction Mappingmentioning

confidence: 90%

“…■ Now we shall present an example where our Theorem 9 can be applied, but the main Theorem 2.2 of Wang and Guo [14] cannot.…”

Section: Fixed Point Theorems For W-cone Distance Contraction Mappingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fixed point theorems for w-cone distance contraction mappings in tvs-cone metric spaces

Ćirić

Lakzian

Rakočević

2012

Fixed Point Theory Appl

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“…In some works, the authors used normal cones to extend some fixed point theorems. Very recently, Wang and Guo [21] introduced the concept of c-distance on a cone metric space, which is a cone version of the w-distance of Kada et.al. [11] and proved a common fixed point theorem for a pair of self mappings in cone metric spaces.…”

Section: Introductionmentioning

confidence: 99%

Some Common Fixed Point Theorems via Generalized c-Distance

Mohanta¹,

Maitra²

2015

Kyungpook mathematical journal

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“…After that, a large number of articles have appeared in studying fixed point, common fixed point, coupled fixed point, common coupled fixed point, tripled fixed point and tripled coincidence point theorems in cone metric spaces under c-distance idea. The reader may see [5,15,17,18,19,42].…”

Section: Introductionmentioning

confidence: 99%

Tripled fixed point theorems in cone metric spaces under F -invariant set and c -distance

Abusalim¹,

Noorani²

2015

J. Nonlinear Sci. Appl.

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The concept of cone metric spaces has been introduced recently as a generalization of metric spaces. The aim of this paper is to give the definitions of F -invariant sets denoted by M in case of M ∈ X 6 in cone and ordered cone version. we also establish some tripled fixed point theorems in cone metric spaces under the concept of an F -invariant set for mappings F : X 3 → X and c-distance on the one hand, and in partially ordered cone metric spaces under the same concepts on the other hand. The present theorems expand and generalize several well-known comparable results in literature in cone metric spaces and ordered cone metric spaces,respectively. An interesting example is given to support our results.

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Distance in cone metric spaces and common fixed point theorems

Cited by 35 publications

References 15 publications

Fixed point theorems for w-cone distance contraction mappings in tvs-cone metric spaces

Fixed point theorems for w-cone distance contraction mappings in tvs-cone metric spaces

Some Common Fixed Point Theorems via Generalized c-Distance

Tripled fixed point theorems in cone metric spaces under F -invariant set and c -distance

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