Fixed point theory in complex valued controlled metric spaces with an application
Open Access
- 1 January 2022
- journal article
- research article
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 7 (7), 11879-11904
- https://doi.org/10.3934/math.2022663
Abstract
In this article we have introduced a metric named complex valued controlled metric type space, more generalized form of controlled metric type spaces. This concept is a new extension of the concept complex valued $ b $-metric type space and this one is different from complex valued extended $ b $-metric space. Using the idea of this new metric, some fixed point theorems involving Banach, Kannan and Fisher contractions type are proved. Some examples togetheran application are described to sustain our primary results.
Keywords
This publication has 23 references indexed in Scilit:
- Controlled Metric Type Spaces and the Related Contraction PrincipleMathematics, 2018
- A Generalization of b-Metric Space and Some Fixed Point TheoremsMathematics, 2017
- "Equation missing" -algebra-valued metric spaces and related fixed point theoremsFixed Point Theory and Applications, 2014
- Common fixed point theorems for multi-valued mappings in complex-valued metric spacesJournal of Inequalities and Applications, 2013
- Common fixed points of almost generalized "Equation missing" -contractive mappings in ordered b-metric spacesFixed Point Theory and Applications, 2013
- Some Common Fixed Point Results for Rational Type Contraction Mappings in Complex Valued Metric SpacesJournal of Operators, 2013
- Common Fixed Point Theorems in Complex Valued Metric SpacesNumerical Functional Analysis and Optimization, 2011
- An Approach to Fixed-Point Theorems on Uniform SpacesTransactions of the American Mathematical Society, 1974
- On Fixed and Periodic Points Under Contractive MappingsJournal of the London Mathematical Society, 1962
- Sur les opérations dans les ensembles abstraits et leur application aux équations intégralesFundamenta Mathematicae, 1922