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5 Demonstratio Mathematica

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Unique common fixed point theorems for pairs of hybrid maps under a new condition in partial metric spaces

100%

Rao K. P. R. , Rao K. R. K.

Demonstratio Mathematica

2014

tom Vol. 47, nr 3

714--724

In this paper, we introduce a new condition namely, ‘condition (W.C.C)’ and obtain two unique common fixed point theorems for pairs of hybrid mappings on a partial Hausdorff metric space without using any continuity and commutativity of the mappings.

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

100%

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

Demonstratio Mathematica

2016

tom 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

84%

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

Demonstratio Mathematica

2014

tom 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.

Fixed point theorems for multivalued mappings in symmetric spaces

84%

Joshi M. , Joshi L. , Dimri R.

Demonstratio Mathematica

2007

tom Vol. 40, nr 3

733-738

In this paper we prove some fixed point theorems for multivalued mappings using rational inequality in a symmetric space. These results are generalizations of some well known results in metric spaces and also in the setting of symmetric spaces.

Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings

67%

Olona M. A. , Alakoya T. O. , Owolabi A.-s. O.-E. , Mewomo O. T.

Demonstratio Mathematica

2021

tom Vol. 54, nr 1

47--67

In this paper, we introduce a shrinking projection method of an inertial type with self-adaptive step size for finding a common element of the set of solutions of a split generalized equilibrium problem and the set of common fixed points of a countable family of nonexpansive multivalued mappings in real Hilbert spaces. The self-adaptive step size incorporated helps to overcome the difficulty of having to compute the operator norm, while the inertial term accelerates the rate of convergence of the proposed algorithm. Under standard and mild conditions, we prove a strong convergence theorem for the problems under consideration and obtain some consequent results. Finally, we apply our result to solve split mixed variational inequality and split minimization problems, and we present numerical examples to illustrate the efficiency of our algorithm in comparison with other existing algorithms. Our results complement and generalize several other results in this direction in the current literature.