Common fixed point theorems for infinite families of contractive maps

Allahyari, Reza; Arab, Reza; Haghighi, Ali Shole

doi:10.1007/s40096-015-0168-3

Cited by 4 publications

(2 citation statements)

References 13 publications

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“…The study of common fixed point for a family of contraction mappings was initiated byĆirić in [1]. Recently, in 2015, Allahyari et al [2] introduced some new type of contractions for a countable family of contraction self-mappings and studied common fixed point for them.…”

Section: Introductionmentioning

confidence: 99%

Common Fixed Point and Endpoint Theorems for a Countable Family of Multi-Valued Mappings

et al. 2020

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Section: Introductionmentioning

confidence: 99%

Common Fixed Point and Endpoint Theorems for a Countable Family of Multi-Valued Mappings

et al. 2020

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“…The existence of a common fixed point for a finite or infinite family of self-mappings and contractive maps is worked by many authors [2,7]. In this way, the existence of a fixed point for infinite families of self-mappings of a complete metric space satisfying some new conditions of common contractivity was studied by Allahyari et al in [3]. Also, the study on fixed point and convergence of sequences generated by a family of k-contractions and ϕ-contractions in Menger spaces was worked by De la Sen et al in [15].…”

Section: Introductionmentioning

confidence: 99%

Existence of common fixed points for linear combinations of contractive maps in enhanced probabilistic metric spaces

Jafari¹,

Shams²,

Ibeas³

et al. 2019

NAMC

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In this paper, we introduce the concept of enhanced probabilistic metric space (briefly EPM-space) as a type of probabilistic metric space. Also, we investigate the existence of fixed points for a (finite or infinite) linear combination of different types of contractive mappings in EPM-spaces. Furthermore, we investigate about the convergence of sequences (generated by a finite or infinite family of contractive mappings) to a common fixed point. The useful application of this research is the study of the stability of switched dynamic systems, where we study the conditions under which the iterative sequences generated by a (finite or infinite) linear combination of mappings (contractive or not), converge to the fixed point. Also, some examples are given to support the obtained results. In the end, a number of figures give us an overview of the examples.

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Fuzzy fixed point theorems and Ulam-Hyers stability of fuzzy set-valued maps

Alansari

Shagari

Azam³

2022

Mathematica Slovaca

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In this paper, new common fuzzy fixed point theorems for sequence of fuzzy set-valued maps in the framework of complete b-metric spaces are established. Consequently, corresponding fixed point theorems in the setting of point-to-set-valued and single-valued mappings are deduced. A few nontrivial examples which dwell upon the generality of our results are provided. Moreover, following the fact that most available Ulam-Hyers type stability results deal with crisp mappings, we initiate the study of stability and well-posedness of functional inclusions involving fuzzy set-valued maps. It is well-known that solution of any functional inclusion is a subset of an appropriate ambient space. With this information, fuzzy fixed point problem for which the right-hand-side is a cut set of a fuzzy set-valued map is introduced. Furthermore, sufficient conditions for existence of solutions of Cantilever Beam Problem and integral inclusions are investigated to indicate the usability of our obtained results.

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Common fixed point theorems for infinite families of contractive maps

Abstract: In this paper, we prove some fixed point theorems for infinite families of self-mappings of a complete metric space satisfying some new conditions of common contractivity. An example is presented to show the effectiveness of our results.

Cited by 4 publications

References 13 publications

Common Fixed Point and Endpoint Theorems for a Countable Family of Multi-Valued Mappings

Common Fixed Point and Endpoint Theorems for a Countable Family of Multi-Valued Mappings

Existence of common fixed points for linear combinations of contractive maps in enhanced probabilistic metric spaces

Fuzzy fixed point theorems and Ulam-Hyers stability of fuzzy set-valued maps

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