Abstract
In this paper, we give a short proof for Reich contraction in rectangular b-metric spaces with increased range of the Lipschtzian constants and illustrate this with a suitable example. Our results generalize, improve and complement several ones in the existing literature.
Highlights
The main result in the paper [5] is the following theorem
In [7], the author has given a positive answer to the Open Question 1 of [5]
Our results improve the results of [4], [5] and [7] in the sense that the range of Lipschitzian constants used have been significantly increased in our results and we have proved the results in a more generalised concept of almost rectangular b-metric space
Summary
The following theorem is the analogue of Reich’s contraction principle in rectangular b-metric space. C2 , for all a, b, c ∈ [0, ∞), we obtain that (X, d) is a complete rectangular b-metric space with coefficient s = 3. From Theorem 2.1 we obtain the following variant of Banach contraction principle in b-rectangular metric spaces. If (X, d) is a complete rectangular b-metric space with coefficient s > 1 and T : X → X is a contraction mapping, T has a unique fixed point x∗, and for any x0 ∈ X the sequence T nx0 converges to x∗. Let (X, d) be a complete rectangular b-metric space with coefficient s > 1 and T : X → X be a mapping satisfying: d(T x, T y) ≤ ad(x, y) + b[d(x, T x) + d(y, T y)].
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
