Fixed point theorems in complex valued metric spaces

Singh, Naval; Singh, Deepak; Badal, Anil; Joshi, Vishal

doi:10.1016/j.joems.2015.04.005

Cited by 28 publications

(26 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The complex valued metric spaces is more general than ordinary metric spaces. According to this concept, a number of articles related to fixed point theory and it's application are presented (see, for example, [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]).…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Urysohn Integral Equations by Fixed Point Technique in Complex Valued Metric Spaces

Hammad

Sen

2019

Mathematics

View full text Add to dashboard Cite

The purpose of this article is to introduce a fixed point result for a general contractive condition in the context of complex valued metric spaces. Also, some important corollaries under this contractive condition are obtained. As an application, we find a unique solution for Urysohn integral equations, and some illustrative examples are given to support our obtaining results. Our results extend and generalize the results of Azam et al. Previous known related results in the literarure and some other known results in the literature.

show abstract

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Urysohn Integral Equations by Fixed Point Technique in Complex Valued Metric Spaces

Hammad

Sen

2019

Mathematics

View full text Add to dashboard Cite

show abstract

“…Recently, Azam et al [3] introduced the concept of complex valued metric spaces which is relatively more general than metric spaces and also proved common fixed point theorems for two mappings satisfying certain rational inequalities. Since then, several papers have dealt with fixed point theory in complex valued metric spaces (see [2,4,5,16,14,22,21,18,19,17,20,23,14] and references cited therein).…”

Section: Introductionmentioning

confidence: 99%

Unified common fixed point theorems in complex valued metric spaces via an implicit relation with applications

Alfaqih¹,

Imdad²,

Rouzkard³

2019

B Soc Paran Mat

View full text Add to dashboard Cite

The purpose of this paper is to prove some common fixed point theorems for two pairs of weakly compatible mappings in complex valued metric spaces satisfying an implicit relation. Several illustrative examples are given which demonstrate the usefulness of our utilized implicit relation. Beside generalizing and improving several well known core results of the existing literature we can deduce several new contractions which have not obtained before in complex valued metric spaces. As an application of our results, we prove the existence and uniqueness of common solution of Hammerstein as well as Urysohn integral equations.

show abstract

“…Recently, Mukheimer [27], Rao et al [35], Dubey et al [14] and Singh et al ( [46], [47]) etc. proved some common fixed point results in complex valued b-metric spaces.…”

Section: Introductionmentioning

confidence: 99%

FIXED POINT THEOREMS USING (CLCS) PROPERTY IN COMPLEX VALUED $b$-METRIC SPACES

Verma¹

2017

FU Math Inform

View full text Add to dashboard Cite

Abstract. Various common fixed point theorems have been proved for one or two pairs of mappings using either (CLR) property ([44]), or by taking one of the range-subspace closed. In this paper, we introduce the notion of (CLCS)-property i.e., "common limit converging in the range sub-space". Using this property, we prove common fixed point theorems for two pairs of weakly compatible mappings in complex valued b-metric spaces satisfying a collection of contractive conditions. Our notion is meaningful and valid because the required common fixed point will always lie on the range-subspace of the mapping-pair. We give some examples to show that if a mapping pair (f, g) on a closed complex valued b-metric space X satisfy the (CLR f ) property, then it is also (CLRg), and vice-versa.

show abstract

Fixed point theorems in complex valued metric spaces

Cited by 28 publications

References 8 publications

Analytical Solution of Urysohn Integral Equations by Fixed Point Technique in Complex Valued Metric Spaces

Analytical Solution of Urysohn Integral Equations by Fixed Point Technique in Complex Valued Metric Spaces

Unified common fixed point theorems in complex valued metric spaces via an implicit relation with applications

FIXED POINT THEOREMS USING (CLCS) PROPERTY IN COMPLEX VALUED $b$-METRIC SPACES

Contact Info

Product

Resources

About