Common Fixed-Point Theorems for Hybrid Generalized (F, 𝜑)-Contractions Under the Common Limit Range Property with Applications

2018 ◽  
Vol 69 (11) ◽  
pp. 1784-1804 ◽  
Author(s):  
H. K. Nashine ◽  
M. Imdad ◽  
M. Ahmadullah
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Common Limit ◽  
The Common ◽  
Common Fixed Point Theorems ◽  
Common Limit Range Property

scholarly journals Common Fixed Point Theorems in Fuzzy Metric Spaces Satisfying -Contractive Condition with Common Limit Range Property

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Sunny Chauhan ◽  
M. Alamgir Khan ◽  
Wutiphol Sintunavarat
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric ◽  
Common Limit ◽  
Common Fixed Point Theorems ◽  
Common Limit Range Property

The objective of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed point in fuzzy metric spaces. Some illustrative examples are furnished which demonstrate the validity of the hypotheses and degree of utility of our results. We derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. As an application to our main result, we prove an integral-type fixed point theorem in fuzzy metric space. Our results improve and extend a host of previously known results including the ones contained in Imdad et al. (2012).

scholarly journals Some Nonunique Common Fixed Point Theorems in Symmetric Spaces through Property

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
E. Karapınar ◽  
D. K. Patel ◽  
M. Imdad ◽  
D. Gopal
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Symmetric Spaces ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
New Class ◽  
The Common ◽  
Common Fixed Point Theorems ◽  
Common Limit Range Property

We introduce a new class of mappings satisfying the “common limit range property” in symmetric spaces and utilize the same to establish common fixed point theorems for such mappings in symmetric spaces. Our results generalize and improve some recent results contained in the literature of metric fixed point theory. Some illustrative examples to highlight the realized improvements are also furnished.

scholarly journals Hybrid Fixed Point Theorems in Symmetric Spaces via Common Limit Range Property

2014 ◽  
Vol 47 (4) ◽  
Author(s):  
Mohammad Imdad ◽  
Sunny Chauhan ◽  
Ahmed H. Soliman ◽  
M. A. Ahmed
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Symmetric Spaces ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Present Form ◽  
Common Limit ◽  
Hybrid Pair ◽  
Common Fixed Point Theorems ◽  
Common Limit Range Property

AbstractIn this paper, we point out that some recent results of Vijaywar et al. (Coincidence and common fixed point theorems for hybrid contractions in symmetric spaces, Demonstratio Math. 45 (2012), 611-620) are not true in their present form. With a view to prove corrected and improved versions of such results, we introduce the notion of common limit range property for a hybrid pair of mappings and utilize the same to obtain some coincidence and fixed point results for mappings defined on an arbitrary set with values in symmetric (semi-metric) spaces. Our results improve, generalize and extend some results of the existing literature especially due to Imdad et al., Javid and Imdad, Vijaywar et al. and some others. Some illustrative examples to highlight the realized improvements are also furnished.

scholarly journals Employing Common Limit Range Property to Prove Unified Metrical Common Fixed Point Theorems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammad Imdad ◽  
Sunny Chauhan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Implicit Function ◽  
Common Limit ◽  
Common Fixed Point Theorems ◽  
Common Limit Range Property

The purpose of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed point in metric spaces satisfying an implicit function essentially due to the paper of Ali and Imdad (2008). As an application to our main result, we derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results including the ones contained in the paper of Ali and Imdad (2008). We also furnish some illustrative examples to support our main results.

scholarly journals Some Integral Type Fixed Point Theorems for Non-Self-Mappings Satisfying Generalized(ψ,φ)-Weak Contractive Conditions in Symmetric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Marwan Amin Kutbi ◽  
Mohammad Imdad ◽  
Sunny Chauhan ◽  
Wutiphol Sintunavarat
Keyword(s):  
Fixed Point ◽  
Symmetric Spaces ◽  
Fixed Point Theorems ◽  
Compatible Mappings ◽  
Integral Type ◽  
Weakly Compatible ◽  
Common Limit ◽  
The Common ◽  
Common Fixed Point Theorems ◽  
Common Limit Range Property

The aim of this paper is to obtain some new integral type fixed point theorems for nonself weakly compatible mappings in symmetric spaces satisfying generalized(ψ,φ)-contractive conditions employing the common limit range property. We furnish some interesting examples which support our main theorems. Our results generalize and extend some recent results contained in Imdad et al. (2013) to symmetric spaces. Consequently, a host of metrical common fixed theorems are generalized and improved. In the process, we also derive a fixed point theorem for four finite families of mappings which can be utilized to derive common fixed point theorems involving any number of finite mappings.

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