New common fixed point theorems and invariant approximation in convex metric spaces

Rouzkard, Fayyaz; Imdad, Mohammad; Nashine, Hemant Kumar

doi:10.36045/bbms/1337864275

Cited by 7 publications

(9 citation statements)

References 11 publications

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“…In the present article, we shall show that there is a gap in the proof of the Theorem 1, which is one of the main results of Rouzkard et al [18]. Then, we obtain a correct version of Theorem 1 by utilizing the concept of (E.A.)…”

Section: Preliminariesmentioning

confidence: 58%

Note on Common Fixed Point Theorems in Convex Metric Spaces

Kumar¹,

Taş

2021

Axioms

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In the present paper, we pointed out that there is a gap in the proof of the main result of Rouzkard et al. (The Bulletin of the Belgian Mathematical Society 2012). Then after, utilizing the concept of (E.A.) property in convex metric space, we obtained an alternative and correct version of this result. Finally, it is clarified that in the theory of common fixed point, the notion of (E.A.) property in the set up of convex metric space develops some new dimensions in comparison to the hypothesis that a range set of one map is contained in the range set of another map.

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Section: Preliminariesmentioning

confidence: 58%

Note on Common Fixed Point Theorems in Convex Metric Spaces

Kumar¹,

Taş

2021

Axioms

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“…A pair of non-compatible or subcompatible mapping satisfies the property (E.A). Obviously, compatible mappings which satisfy the property (E.A) are subcompatible but the converse statement does not hold in general (see [49,Example 2.3]). Two occasionally weakly compatible mappings are subcompatible, however the converse is not true in general (see [18,Example 1.2]).…”

Section: Definition 4 ([4]mentioning

confidence: 99%

Common fixed point theorems satisfying integral type rational contractive conditions and applications

Nashine¹

2015

MMN

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Inspired by the concept of integral type (Branciari type) contractive condition and respective fixed point results, we derive some new common fixed point theorems for quadruple self mappings satisfying a generalized W-contractive condition or a generalized-contractive condition of integral type, also using the notions of compatibility and subsequential continuity (alternately subcompatibility and reciprocal continuity) in the frame of metric spaces. We furnish some examples to illustrate the useability of our main results. Several results existing in the literature are obtained as consequences of the main results. At the end of this article the existence and uniqueness of solutions for certain systems of integral equations and functional equations arising in dynamic programming are demonstrated with the help of the obtained results.

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“…A pair of subcompatible mappings satisfies the property (E.A). Obviously, compatible mappings which satisfy the property (E.A) are subcompatible, but the converse statement does not hold in general (see [36,Example 2.3]). Two occasionally weakly compatible mappings are subcompatible; however, the converse is not true in general (see […”

Section: Examples 21 and 22])mentioning

confidence: 99%

“…The authors would like to thank Professor Mohammad Imdad for the preprint of paper [36] and anonymous referees for their valuable comments that helped them to improve the exposition, in particular for Remark 16. The second author is thankful to the Ministry of Education, Science and Technological Development of Serbia.…”

Section: Acknowledgmentsmentioning

confidence: 99%