Periodic points of rational inequality in a complex valued metric space

In this paper, we shall prove some periodic point theorems of rational inequality in complex valued metric spaces. The first result of this type was due to Sehgal[14] and his result was generalized by Guseman[5], Khanzanchi[6], Rhoades and Ray[2] and Murthy and Pathak[10].

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Some Common Coupled Fixed Point Results for Generalized Contraction in Complex-Valued Metric Spaces

Journal of Applied Mathematics ◽

10.1155/2013/352927 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 6

Author(s):

Marwan Amin Kutbi ◽

Akbar Azam ◽

Jamshaid Ahmad ◽

Cristina Di Bari

Keyword(s):

Fixed Points ◽

Metric Space ◽

Metric Spaces ◽

Coupled Fixed Point ◽

Generalized Contraction ◽

Complex Valued Metric Space ◽

The Common ◽

Complex Valued ◽

Common Coupled Fixed Points ◽

Coupled Fixed Points

We introduce and study the notion of common coupled fixed points for a pair of mappings in complex valued metric space and demonstrate the existence and uniqueness of the common coupled fixed points in a complete complex-valued metric space in view of diverse contractive conditions. In addition, our investigations are well supported by nontrivial examples.

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The periodic points of ε-contractive maps in fuzzy metric spaces

Applied General Topology ◽

10.4995/agt.2021.14449 ◽

2021 ◽

Vol 22 (2) ◽

pp. 311

Author(s):

Taixiang Sun ◽

Caihong Han ◽

Guangwang Su ◽

Bin Qin ◽

Lue Li

Keyword(s):

Periodic Point ◽

Metric Space ◽

Metric Spaces ◽

Periodic Points ◽

Fuzzy Metric Space ◽

Connected Component ◽

Fuzzy Metric Spaces ◽

Fuzzy Metric ◽

Contractive Maps

<p>In this paper, we introduce the notion of ε-contractive maps in fuzzy metric space (X, M, ∗) and study the periodicities of ε-contractive maps. We show that if (X, M, ∗) is compact and f : X −→ X is ε-contractive, then P(f) = ∩ ∞n=1f n (X) and each connected component of X contains at most one periodic point of f, where P(f) is the set of periodic points of f. Furthermore, we present two examples to illustrate the applicability of the obtained results.</p>

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Common Fixed Points for Multivalued Mappings in Complex Valued Metric Spaces with Applications

Abstract and Applied Analysis ◽

10.1155/2013/854965 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12 ◽

Cited By ~ 6

Author(s):

Jamshaid Ahmad ◽

Chakkrid Klin-Eam ◽

Akbar Azam

Keyword(s):

Fixed Point ◽

Metric Space ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Common Fixed Points ◽

Multivalued Mappings ◽

Contractive Mappings ◽

Complex Valued Metric Space ◽

Complex Valued ◽

Common Fixed Point Theorems

In this paper, we introduce the notion of multivalued contractive mappings in complex valued metric space and prove common fixed point theorems for two multivalued contractive mappings in complex valued metric spaces without using the notion of continuity. Our results improve and extend the results of Azam et al. (2011).

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Common Fixed Point Results for Fuzzy Mappings on Complex-Valued Metric Spaces with Homotopy Results

Symmetry ◽

10.3390/sym11010061 ◽

2019 ◽

Vol 11 (1) ◽

pp. 61 ◽

Cited By ~ 1

Author(s):

Humaira ◽

Muhammad Sarwar ◽

Poom Kumam

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Metric Space ◽

Metric Spaces ◽

Contractive Condition ◽

Rational Expression ◽

Complex Valued Metric Space ◽

Homotopy Result ◽

Complex Valued

Owing to the notion of a complex-valued metric space, we prove fixed point results, which generalize some common fixed point results under contractive condition for rational expression in the context of complex-valued metric spaces. In application, we present a homotopy result to apply the results obtained herein.

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Common fixed point results in complex valued metric spaces with application to integral equations

Filomat ◽

10.2298/fil1407363h ◽

2014 ◽

Vol 28 (7) ◽

pp. 1363-1380 ◽

Cited By ~ 4

Author(s):

N. Hussain ◽

Akbar Azam ◽

Jamshaid Ahmad ◽

Muhammad Arshad

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Integral Equations ◽

Metric Space ◽

Metric Spaces ◽

Contractive Condition ◽

Complex Valued Metric Space ◽

Complex Valued

In this paper, common fixed point of six mappings satisfying a contractive condition involving rational inequality in the framework of complex valued metric space are obtained. Moreover, some examples and applications to integral equations are given here to illustrate the usability of the obtained results.

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Fixed Point Theorems in Complex Valued B-Metric Spaces

CAUCHY ◽

10.18860/ca.v4i4.3669 ◽

2017 ◽

Vol 4 (4) ◽

pp. 138

Author(s):

Dahliatul Hasanah

Keyword(s):

Fixed Point ◽

Metric Space ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Complex Valued Metric Space ◽

Complex Valued

A complex-valued b-metric space is a generalization of a b-metric space in which its b-metric space has complex value. It can also be considered as a generalization of a complex-valued metric space. Hence, fixed point theorems that have been studied in b-metric spaces are now of interest whether the theorems are applicable in complex-valued b-metric spaces. In this paper we have obtained some fixed point theorems in complex-valued b-metric spaces. The theorems are derived from the corresponding theorems in b-metric spaces.

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FIXED POINT THEORY IN COMLEX VALUED METRIC SPACE

Journal of University of Shanghai for Science and Technology ◽

10.51201/jusst/21/07232 ◽

2021 ◽

Vol 23 (07) ◽

pp. 846-852

Author(s):

Abhishek Koundal ◽

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Metric Space ◽

Metric Spaces ◽

Fixed Point Theory ◽

Point Theory ◽

Distance Functions ◽

Control Functions ◽

Complex Valued Metric Space ◽

Complex Valued

The aim of this paper is to establish and prove several results on a common fixed point for a pair of mappings satisfying more general contraction conditions portrayed by rational expressions having point-dependent control functions as coefficients in complex-valued metric spaces. Fixed point theory in complex-valued metric space using contractive conditions, rational inequality, common limit range property for two pairs of mapping deriving common fixed-point results under a generalized altering distance functions, E.A and CLR property. Obtaining consecutive approximations to the fixed point of an approximate mapping is the goal of a variety of processes in numerical analysis and approximation theory. Our goal in this paper is to examine fixed point theory and its applications in metric spaces, as well as to develop several fixed-point theorems in entire metric spaces that generalize many renowned mathematicians’ achievements.

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Best Proximity Point Results in Complex Valued Metric Spaces

International Journal of Analysis ◽

10.1155/2014/827862 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Binayak S. Choudhury ◽

Nikhilesh Metiya ◽

Pranati Maity

Keyword(s):

Minimum Distance ◽

Metric Spaces ◽

Optimal Solution ◽

Global Optimal Solution ◽

Complex Valued Metric Space ◽

Fixed Point Equation ◽

Point Equation ◽

Global Optimal ◽

Metric Function ◽

Complex Valued

We introduce the concept of proximity points for nonself-mappings between two subsets of a complex valued metric space which is a recently introduced extension of metric spaces obtained by allowing the metric function to assume values from the field of complex numbers. We apply this concept to obtain the minimum distance between two subsets of the complex valued metric spaces. We treat the problem as that of finding the global optimal solution of a fixed point equation although the exact solution does not in general exist. We also define and use the concept of P-property in such spaces. Our results are illustrated with examples.

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Common Fixed Point Results for Six Mappings via Integral Contractions with Applications

International Journal of Analysis ◽

10.1155/2016/7480469 ◽

2016 ◽

Vol 2016 ◽

pp. 1-13 ◽

Cited By ~ 1

Author(s):

Mian Bahadur Zada ◽

Muhammad Sarwar ◽

Nayyar Mehmood

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Type Inequality ◽

Dynamical Programming ◽

System Of Functional Equations ◽

Complex Valued Metric Space ◽

Complex Valued ◽

Common Fixed Point Theorems

Common fixed point theorems for six self-mappings under integral type inequality satisfying (E.A) and (CLR) properties in the context of complex valued metric space (not necessarily complete) are established. The derived results are new even for ordinary metric spaces. We prove existence result for optimal unique solution of the system of functional equations used in dynamical programming with complex domain.

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Fuzzy Fixed Point Results For Φ Contractive Mapping with Applications

Complexity ◽

10.1155/2018/5303815 ◽

2018 ◽

Vol 2018 ◽

pp. 1-12 ◽

Cited By ~ 2

Author(s):

Humaira ◽

Muhammad Sarwar ◽

G. N. V. Kishore

Keyword(s):

Fixed Point ◽

Metric Space ◽

Contractive Mapping ◽

Contractive Mappings ◽

Fixed Point Result ◽

Control Functions ◽

Complex Valued Metric Space ◽

Fuzzy Fixed Point ◽

Complex Valued ◽

Rational Type

In this paper, using rational type contractions, common fuzzy fixed point result for Φ contractive mappings involving control functions as coefficients of contractions in the setting of complex-valued metric space is established. The derived results generalizes some result in the existing literature. To show the validity of the derived results an appropriate example and applications are also discussed.

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