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Fuzzy fixed point results with rational type contractions in partially ordered complex-valued metric spaces

Sarwar M., Humaira H., Huang H.

Commentationes Mathematicae

2018

Vol. 58, No. 1/2

57--78

In this manuscript, some fixed point results for fuzzy mappings with rational type contraction in the context of a complete partially ordered complex-valued metric space are established. The derived results generalize some fixed point theorems in the existing literature. An appropriate example is given.

Strict contractive conditions and common fixed point theorems with application

Pant V.

Demonstratio Mathematica

2013

Vol. 46, nr 2

405--413

The aim of the present paper is to obtain common fixed point theorems under a strict contractive condition by assuming minimal commutativity conditions. Our theorems extend the results due to Pant and Pant [4]. In the setting of our results, we also provide pair of mappings which ensures the existence of a common fixed point; however, both the mappings are discontinuous at the common fixed point. We, thus, provide one more answer to the problem of Rhoades [10]. In the last section, we apply our results to solve an eigenvalue problem.

Common fixed points of mappings not satisfying contractive condition

Pant V., Padaliya S., Pant R. P.

Fasciculi Mathematici

2008

Nr 40

71-77

The aim of this paper is to consider a new approach for obtaining common fixed point theorems in metric spaces by subjecting the triangle inequality to a Lipschitz type condition. For values of the Lipschitz constant k < 1/3 the condition reduces to a Banach type contractive condition and we get the results known so far. However, values of k ≥ 1/3 yield new result. It may be observed that in the setting of metric spaces k ≥ 1/3 generally does not ensure the existence of fixed points and there is no known method for dealing these cases. In Theorem 1 and Theorem 2 we provide results under a new condition. In the last section of this paper (Theorem 3 and Theorem 4) by using the (E.A) property introduced by Aamri and Moutawakil [2] we extend the results obtained in Theorem 1 and Theorem 2.

A note on the theorem of V. Berinde

Rafiq A.

Demonstratio Mathematica

2006

Vol. 39, nr 4

863-867

V. Berinde presented convergence theorem [1] in normed spaces for Ishikawa iterations associated with Zamfirescue operators, which is an extension of the theorem of Rhoades [11]. In this note, we point out some misprints in the calculations and established new inequalities involved in the proof of the theorem. Consequently we give better estimation in proving the convergence theorem.