Common solution of Urysohn integral equations with the help of common fixed point results in complex valued metric spaces

Sintunavarat, Wutiphol; Zada, Mian Bahadur; Sarwar, Mohammed

doi:10.1007/s13398-016-0309-z

Cited by 11 publications

(7 citation statements)

References 13 publications

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“…Many researchers study the applications of common fixed point theorems in complex valued metric spaces; see for instance [17,18] and the references therein. On the other hand, Liu et al [19] and Sarwar et al [20] study the existence and uniqueness of common solution for the system of functional equations arising in dynamic programming with real domain.…”

Section: Applicationsmentioning

confidence: 99%

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

Zada

Sarwar

Mehmood

2016

International Journal of Analysis

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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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Section: Applicationsmentioning

confidence: 99%

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

Zada

Sarwar

Mehmood

2016

International Journal of Analysis

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“…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

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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.

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“…In 2011, Azam et.al [2] introduced the concept of complex valued metric spaces which is a generalization of metric spaces and established common fixed point of self-mappings satisfying generalized contractive condition. Many authors (see [2,7,[9][10][11]) have obtained fixed point results in complex valued metric spaces and proved the existence and uniqueness of solution of nonlinear integral equations.…”

Section: Introductionmentioning

confidence: 99%

Common Fixed Point results in Complex valued metric spaces via simulation functions

Gupta¹,

Rohilla²

2019

Preprint

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In this paper, the notion of C-simulation function is introduced and the existence and uniqueness of common fixed points of two self-mappings satisfying contractive conditions in the setting of complex valued metric spaces via C-simulation functions are studied. Examples are also provided to demonstrate the results. The existence and uniqueness of a first-order periodic differential equation is also obtained as an application of the result.

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Common solution of Urysohn integral equations with the help of common fixed point results in complex valued metric spaces

Cited by 11 publications

References 13 publications

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

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

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

Common Fixed Point results in Complex valued metric spaces via simulation functions

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