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Common fixed point theorems for mappings under (CLRS)-property in partial metric spaces

Rao K. P. R., Imdad M., Siva Parvathi K. V.

Demonstratio Mathematica

2016

Vol. 49, nr 3

357--371

In this paper, we introduce the concept of (CLRS)-property for mappings F : X x X → X and S : X → X (wherein X stands for a partial metric space) and utilize the same to prove two common fixed point theorems for two pairs of mappings in partial metric spaces. We also furnish two examples to illustrate our main theorems.

A Suzuki type unique common fixed point theorem for two pairs of hybrid maps under a new condition in partial metric spaces

Rao K. P. R., Rao K. R. K., Imdad M.

Demonstratio Mathematica

2016

Vol. 49, nr 1

79--94

In this paper, we introduce a new condition namely: condition (W.C.C.) and utilize the same to prove a Suzuki type unique common fixed point theorem for two hybrid pairs of mappings in partial metric spaces employing the partial Hausdorff metric which generalizes several known results of the existing literature proved in metric and partial metric spaces.

Hybrid fixed point theorems in symmetric spaces via common limit range property

Imdad M., Chauhan S., Soliman A. H., Ahmed M. A.

Demonstratio Mathematica

2014

Vol. 47, nr 4

949--962

In 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.