On the generalized 𝐂∗- valued metric spaces related with Banach fixed point theory

Özer, Özen; Omran, Saleh

International Journal of Advanced and Applied Sciences

Int. j. adv. appl. sci.

EISSN: 2313-3724

Print ISSN: 2313-626X

Volume 4, Issue 2 (February 2017), Pages: 35-37

Title: On the generalized 𝐂∗- valued metric spaces related with Banach fixed point theory

Author(s): Özen Özer ^1,*, Saleh Omran ^{2, 3}

Affiliation(s):

¹Department of Mathematics, Faculty of Science and Arts, Kırklareli University 39100, Kirklareli, Turkey
²Department of Mathematics, Faculty of Science, Taif University, Taif, Saudi Arabia
³Department of Mathematics, South Valley University, Quena, Egypt

https://doi.org/10.21833/ijaas.2017.02.006

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Abstract:

The Banach contraction principle, which shows that every contractive mapping has a unique fixed point in a complete metric space, has been extended in many directions. One of the branches of this theory is devoted to the study of fixed points. Especially, Fixed point theory in - algebra valued metric spaces has greatly developed in recent times. Also, we study on generalized - algebra valued metric space and give some examples, the idea of this metric is to replace the set of real numbers by the positive cone - algebras, the set of positive elements on the - algebras the notation introduced recently. Also, we prove certain fixed-point theorem for a single-valued mapping in such spaces. The mapping we consider here is assumed to satisfy certain ‑metric conditions with generalized fixed-point theorem. Moreover, the paper provides an application to prove the existence and uniqueness of fixed points.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Fixed point theory, 𝐂∗- algebra, Positive cone

Article History: Received 24 November 2016, Received in revised form 27 January 2017, Accepted 28 January 2017

Digital Object Identifier:

https://doi.org/10.21833/ijaas.2017.02.006

Citation:

Özer Ö and Omran S (2017). On the generalized 𝐂∗- valued metric spaces related with Banach fixed point theory. International Journal of Advanced and Applied Sciences, 4(2): 35-37

http://www.science-gate.com/IJAAS/V4I2/Ozer.html

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