<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The main goal of this study is to define a new metric space which is a generalization of complex valued metric spaces introduced by Azam et al. [1] using the set of elliptic numbers<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_auom-2021-0011_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><msub><mrow><mi>𝔼</mi></mrow><mi>p</mi></msub><mo>=</mo><mrow><mo>{</mo><mrow><mo>∈</mo><mo>=</mo><mi>υ</mi><mo>+</mo><mi>i</mi><mi>ω</mi><mo>:</mo><mi>υ</mi><mo>,</mo><mi>ω</mi><mo>∈</mo><mi>ℝ</mi><mo>,</mo><mi> </mi><mi> </mi><msup><mrow><mi>i</mi></mrow><mn>2</mn></msup><mo>=</mo><mi>p</mi><mo>&lt;</mo><mn>0</mn></mrow><mo>}</mo></mrow><mo>,</mo></mrow></math><tex-math>{\mathbb{E}_p} = \left\{ { \in  = \upsilon  + i\omega :\upsilon ,\omega  \in \mathbb{R},\,\,{i^2} = p &lt; 0} \right\},</tex-math></alternatives></disp-formula>
and this space is named as an elliptic valued metric space. Some topological properties of this new space are examined. Also, some fixed point results are established in the setting of elliptic valued metric spaces by introducing new classes of mappings which the obtained results are real generalizations of the consequences of several fixed point theorems in the existing literature.</p></abstract>

The main goal of this study is to define a new metric space which is a generalization of complex valued metric spaces introduced by Azam et al. [1] using the set of elliptic numbers𝔼p={∈=υ+iω:υ,ω∈ℝ,  i2=p<0},{\mathbb{E}_p} = \left\{ { \in  = \upsilon  + i\omega :\upsilon ,\omega  \in \mathbb{R},\,\,{i^2} = p < 0} \right\},
and this space is named as an elliptic valued metric space. Some topological properties of this new space are examined. Also, some fixed point results are established in the setting of elliptic valued metric spaces by introducing new classes of mappings which the obtained results are real generalizations of the consequences of several fixed point theorems in the existing literature.

Coincidence and Common Fixed Point Theorems via ϱ-Class Functions in Elliptic Valued Metric Spaces

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The main goal of this study is to define a new metric space which is a generalization of complex valued metric spaces introduced by Azam et al. [1] using the...

Coincidence and Common Fixed Point Theorems via ϱ-Class Functions in Elliptic Valued Metric Spaces

Published Online: Apr 13, 2021

Page range: 165 - 182

Received: Jun 25, 2020

Accepted: Aug 01, 2020

DOI: https://doi.org/10.2478/auom-2021-0011

Keywords
Elliptic valued metric space, Common fixed point, ϱ-class Functions, Weakly Compatible Mappings

© 2021 Mahpeyker Öztürk et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Coincidence and Common Fixed Point Theorems via ϱ-Class Functions in Elliptic Valued Metric Spaces

Published Online: Apr 13, 2021

Page range: 165 - 182

Received: Jun 25, 2020

Accepted: Aug 01, 2020

DOI: https://doi.org/10.2478/auom-2021-0011

KeywordsElliptic valued metric space, Common fixed point, ϱ-class Functions, Weakly Compatible Mappings

© 2021 Mahpeyker Öztürk et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Elliptic valued metric space, Common fixed point, ϱ-class Functions, Weakly Compatible Mappings