scholarly journals Unified Common Fixed Point Theorems for a Hybrid Pair of Mappings via an Implicit Relation Involving Altering Distance Function

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Sunny Chauhan ◽  
Muhammad Alamgir Khan ◽  
Zoran Kadelburg ◽  
Mohammad Imdad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Distance Function ◽  
Altering Distance Function ◽  
Implicit Relation ◽  
Altering Distance ◽  
Hybrid Pair ◽  
Common Fixed Point Theorems ◽  
Common Limit Range Property

The object of this paper is to emphasize the role of a suitable implicit relation involving altering distance function which covers a multitude of contraction conditions in one go. By using this implicit relation, we prove a new coincidence and common fixed point theorem for a hybrid pair of occasionally coincidentally idempotent mappings in a metric space employing the common limit range property. Our main result improves and generalizes a host of previously known results. We also utilize suitable illustrative examples to substantiate the realized improvements in our results.

scholarly journals Common Fixed Point Theorems in Metric Space by Altering Distance Function

2017 ◽  
Vol 07 (06) ◽  
pp. 335-344
Author(s):  
Vishnu Narayan Mishra ◽  
Balaji Raghunath Wadkar ◽  
Ramakant Bhardwaj ◽  
Idrees A. Khan ◽  
Basant Singh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Distance Function ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Altering Distance Function ◽  
Altering Distance ◽  
Common Fixed Point Theorems

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 Common fixed points of single-valued and multivalued maps

2005 ◽  
Vol 2005 (19) ◽  
pp. 3045-3055 ◽  
Author(s):  
Yicheng Liu ◽  
Jun Wu ◽  
Zhixiang Li
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Common Fixed Points ◽  
Partial Answer ◽  
Multivalued Maps ◽  
Hybrid Pair ◽  
Common Fixed Point Theorems

We define a new property which contains the property (EA) for a hybrid pair of single- and multivalued maps and give some new common fixed point theorems under hybrid contractive conditions. Our results extend previous ones. As an application, we give a partial answer to the problem raised by Singh and Mishra.

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