Wyniki wyszukiwania - BazTech

1

Strict contractive conditions and common fixed point theorems with application

Pant V.

Demonstratio Mathematica

|

2013

|

Vol. 46, nr 2

405--413

EN

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.

2

(ε, δ) contractive condition and common fixed points

Pant V., Jha K.

Fasciculi Mathematici

|

2009

|

Nr 42

73-84

EN

In the present paper we prove a common fixed point theorem (Theorem 1) for four mappings under the (ε, δ) contractive condition, however, without either imposing any additional restriction on δ or assuming the ∅-contractive condition together with. While proving the theorem, neither the completeness of the metric space is assumed nor any of the mappings is required to be continuous. Thus we also provide one more answer to the problem of Rhoades [24] which ensures the existence of common fixed point, however, does not force the maps to be continuous at the common fixed point. Theorem 2 generalizes further the result obtained in Theorem 1.

3

Common fixed points of mappings not satisfying contractive condition

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

Fasciculi Mathematici

|

2008

|

Nr 40

71-77

EN

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.