On nearly Menger and nearly star-Menger spaces

In 1999, Kocinac defined and characterized the almost Menger property. Following this concept, we define and investigate nearly Menger and nearly star-Menger spaces. Every Menger space is nearly Menger, and every nearly Menger space is almost Menger. It is demonstrated that a nearly Menger space may not necessarily be a Menger space. In the similar way, we consider nearly ?-sets.

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n-Tupled Coincidence Point Theorems for Probabilistic ψ-Contractions in Menger Spaces

International Journal of Computational Mathematics ◽

10.1155/2016/7109190 ◽

2016 ◽

Vol 2016 ◽

pp. 1-14 ◽

Cited By ~ 1

Author(s):

Penumarthy Parvateesam Murthy ◽

Uma Devi Patel

Keyword(s):

Fixed Point ◽

Fixed Point Theorems ◽

Coincidence Point ◽

Gauge Function ◽

Triangular Norm ◽

Menger Space ◽

Menger Spaces ◽

Weak Compatibility

We introduced n-tupled coincidence point for a pair of maps T:Xn→X and A:X→X in Menger space. Utilizing the properties of the pseudometric and the triangular norm, we will establish n-tupled coincidence point theorems under weak compatibility as well as n-tupled fixed point theorems for hybrid probabilistic ψ-contractions with a gauge function. Our main results do not require the conditions of continuity and monotonicity of ψ. At the end of this paper, an example is given to support our main theorem.

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Common fixed point theorems in Menger spaces

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/ijmms/2006/75931 ◽

2006 ◽

Vol 2006 ◽

pp. 1-15

Author(s):

Chi-Ming Chen ◽

Tong-Huei Chang

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Fixed Point Theorems ◽

Contractive Condition ◽

Menger Space ◽

Menger Spaces ◽

Set Valued Mappings ◽

Common Fixed Point Theorems

We proved two common fixed point theorems for four self-mappings and two set-valued mappings withφ-contractive condition in a Menger space.

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Common Fixed Point Theorems Using the E.A. and CLR Properties in 2-Menger Spaces

International Journal of Analysis ◽

10.1155/2013/934738 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7

Author(s):

Balbir Singh ◽

Vishal Gupta ◽

Sanjay Kumar

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Common Fixed Point ◽

Point Theorem ◽

Compatible Maps ◽

Weakly Compatible Maps ◽

Menger Space ◽

Weakly Compatible ◽

Menger Spaces ◽

Common Fixed Point Theorem

First, we prove a common fixed point theorem using weakly compatible maps in 2-Menger space with t-norm of Hadzic type. Second, we prove a common fixed point theorem using the E.A. property along with weakly compatible maps. Further, we obtained a common fixed point theorem using the CLR property along with weakly compatible maps. At the end, we provide an application of our main theorem for four finite families of mappings.

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On common fixed points in generalized Menger spaces

International Journal of Applied Mathematical Research ◽

10.14419/ijamr.v5i4.6721 ◽

2016 ◽

Vol 5 (4) ◽

pp. 197

Author(s):

Salwa Abed ◽

Hadeel Hussein Luaibi

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Metric Space ◽

Fixed Point Theorems ◽

Suitable Condition ◽

Common Fixed Points ◽

Menger Space ◽

Iteration Sequence ◽

Menger Spaces ◽

Common Fixed Point Theorems

R. Vasuki [1] proved fixed point theorems for expansive mappings in Menger spaces. R. Gujetiya and et al [2] presented an extension of the main result of Vasuki, for four expansive mappings in Menger space. In this article, an important lemma is given to prove that the iteration sequence is Cauchy under suitable condition in Menger probabilistic G-metric space (shortly, MPGM-space). And then, used to obtain three common fixed point theorems for expansive type mappings.

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