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Your search keyword '"Mani, Gunaseelan"' showing total 189 results
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189 results on '"Mani, Gunaseelan"'

5. Solving system of Urysohn type integral equation via bicomplex partial b-metric space

Author

Mani, Gunaseelan, Gnanaprakasam, Arul Joseph, Li, Yongjin, and Gu, Zhaohui

Subjects
Mathematics - Functional Analysis
Abstract

In this paper, we introduce the notion of bicomplex partial b-metric space and prove some common fixed point theorems. Our results generalize and expand some of the literature's well known results. We also explore some of the applications of our key results to Urysohn type integral equations.

Published
2021

7. Some common fixed point theorem of rational contractive mappings in dislocated metric spaces

Author

Jeevanandam Uma Maheswari, Annadurai Anbarasan, Mani Gunaseelan, and Kumar Santosh

Subjects
fixed point, dislocated metric spaces, common fixed point, 47h09, 47h10, Mathematics, QA1-939
Abstract

We improve the rational contractive condition and prove the common fixed point in the dislocated metric spaces. In addition, the new generalized rational contraction has existence of a common solution for a system of integral equations.

Published
2023
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10. A study of neutrosophic controlled pentagonal metric space with applications.

Author

Mani, Gunaseelan, Raj Michael, Edwin Antony, Ganesh, Purushothaman, Thabet, Sabri T. M., Kedim, Imed, and Vivas-Cortez, Miguel

Subjects
METRIC spaces, FRACTIONAL differential equations
Abstract

In this manuscript, we present the concept of neutrosophic controlled pentagonal metric space (NCPMS), and prove some new fixed point results. Furthermore, we established many interesting outcomes for contraction maps. At last, we show the uniqueness and existence results for fractional differential and integral equations to illustrate the validity of the main outcomes. [ABSTRACT FROM AUTHOR]

Published
2024
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11. Solving system of linear equations via bicomplex valued metric space

Author

Gnanaprakasam Arul Joseph, Boulaaras Salah Mahmoud, Mani Gunaseelan, Cherif Bahri, and Idris Sahar Ahmed

Subjects
bicomplex valued metric space, common fixed point linear equation, 47h9, 47h10, 30g35, 46n99, 54h25, Mathematics, QA1-939
Abstract

In this paper, we prove some common fixed point theorems on bicomplex metric space. Our results generalize and expand some of the literature’s well-known results. We also explore some of the applications of our key results.

Published
2021
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12. Solution of integral equations via coupled fixed point theorems in 𝔉-complete metric spaces

Author

Mani Gunaseelan, Gnanaprakasam Arul Joseph, Lee Jung Rye, and Park Choonkil

Subjects
orthogonal set, orthogonal metric space, orthogonal continuous, orthogonal preserving, orthogonal 𝔉-contraction, coupled fixed point, 47h10, 54h25, Mathematics, QA1-939
Abstract

The concept of coupled 𝔉-orthogonal contraction mapping is introduced in this paper, and some coupled fixed point theorems in orthogonal metric spaces are proved. The obtained results generalize and extend some of the well-known results in the literature. An example is presented to support our results. Furthermore, we apply our result to obtain the existence theorem for a common solution of the integral equations: ζ(v)=ð(v)+∫0MΞ(v,β)Ω(β,ζ(β),ξ(β))dβ,v∈[0,H],ξ(v)=ð(v)+∫0MΞ(v,β)Ω(β,ξ(β),ζ(β))dβ,v∈[0,H],\left\{\begin{array}{ll}\zeta \left({\mathfrak{v}})=ð\left({\mathfrak{v}})+\underset{0}{\overset{{\mathfrak{M}}}{\displaystyle \int }}\Xi \left({\mathfrak{v}},\beta )\Omega \left(\beta ,\zeta \left(\beta ),\xi \left(\beta )){\rm{d}}\beta ,& {\mathfrak{v}}\in \left[0,{\mathscr{H}}],\\ \xi \left({\mathfrak{v}})=ð\left({\mathfrak{v}})+\underset{0}{\overset{{\mathfrak{M}}}{\displaystyle \int }}\Xi \left({\mathfrak{v}},\beta )\Omega \left(\beta ,\xi \left(\beta ),\zeta \left(\beta )){\rm{d}}\beta ,& {\mathfrak{v}}\in \left[0,{\mathscr{H}}],\end{array}\right. where (a)ð:M→Rð:{\mathfrak{M}}\to {\mathbb{R}} and Ω:M×R×R→R\Omega :{\mathfrak{M}}\times {\mathbb{R}}\times {\mathbb{R}}\to {\mathbb{R}} are continuous;(b)Ξ:M×M\Xi :{\mathfrak{M}}\times {\mathfrak{M}} is continuous and measurable at β∈M,∀\beta \in {\mathfrak{M}},\hspace{0.33em}\forall v∈M{\mathfrak{v}}\in {\mathfrak{M}};(c)Ξ(v,β)≥0,∀v,β∈M\Xi \left({\mathfrak{v}},\beta )\ge 0,\hspace{0.33em}\forall {\mathfrak{v}},\beta \in {\mathfrak{M}} and ∫0HΞ(v,β)dβ≤1,∀v∈M{\int }_{0}^{{\mathscr{H}}}\Xi \left({\mathfrak{v}},\beta ){\rm{d}}\beta \le 1,\hspace{0.33em}\forall {\mathfrak{v}}\in {\mathfrak{M}}.

Published
2021
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15. On new common fixed point theorems via bipolar fuzzy b-metric space with their applications.

Author

Maheswari, J. Uma, Dillibabu, K., Mani, Gunaseelan, Thabet, Sabri T. M., Kedim, Imed, and Vivas-Cortez, Miguel

Subjects
FRACTIONAL differential equations, CONTRACTIONS (Topology)
Abstract

This research work is devoted to investigating new common fixed point theorems on bipolar fuzzy b -metric space. Our main findings generalize some of the existence outcomes in the literature. Furthermore, we illustrate our findings by providing some applications for fractional differential and integral equations. [ABSTRACT FROM AUTHOR]

Published
2024
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16. EXPLORING THE ALGEBRAIC AND TOPOLOGICAL PROPERTIES OF SEMIGROUPS THROUGH THEIR PRIME m-BI IDEALS.

Author

MUNIR, MOHAMMAD, KAUSAR, NASREEN, ANITHA, K., MANI, GUNASEELAN, and TEHREEM

Subjects
PRIME ideals, TOPOLOGICAL property, TOPOLOGY
Abstract

We introduce the concepts of the prime m-bi ideal and their associated types in the semigroups. Different characterizations of the semigroups using these m-bi ideals are presented. The forms of the topologies induced by the prime and strongly prime m-bi ideals in the semigroups are also explored. The result shows that either both the conditions of m-regularity and m-intraregularity or existence of pairwise comaximal m-bi ideals in a semigroup is necessary for strongly prime m-bi ideals to induce a topology; whereas the existence of pairwise comaximal m-bi ideals is necessary for the prime m-bi ideals to induce topology on the semigroups. We concluded that the prime m-bi ideals are as important to study the semigroups as the prime bi ideals. [ABSTRACT FROM AUTHOR]

Published
2024
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17. Solution of a nonlinear fractional-order initial value problem via a C∗-algebra-valued R-metric space.

Author

Janardhanan, Gopinath, Mani, Gunaseelan, Michael, Edwin Antony Raj, Thabet, Sabri T. M., and Kedim, Imed

Subjects
INITIAL value problems
Abstract

In this article, we prove new common fixed-point theorems on a C ∗ -algebra-valued R -metric space. An example is given based on our obtained results. To enhance our results, a strong application based on the fractional-order initial value problem is provided. [ABSTRACT FROM AUTHOR]

Published
2024
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39. Solution of Nonlinear Fredholm Integral Equations on Almost Z⊥-Contraction

Author

Nallaselli, Gunasekaran, Gnanaprakasam, Arul Joseph, Mani, Gunaseelan, Javed, Khalil, and Almalki, Yahya

Subjects
Article Subject
Abstract

In this manuscript, we develop an orthogonal to basically Z-contraction and demonstrate various fixed point theorems of nonlinear Fredholm integral equation solutions in such a contraction. By using these ideas of discovering the fixed point theorems, we can also build the application of the Fredholm integral equation.

Published
2023
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40. Applications to Nonlinear Fractional Differential Equations via Common Fixed Point on ℂ ★ -Algebra-Valued Bipolar Metric Spaces.

Author

Mani, Gunaseelan, Gnanaprakasam, Arul Joseph, Subbarayan, Poornavel, Chinnachamy, Subramanian, George, Reny, and Mitrović, Zoran D.

Subjects
*FIXED point theory, *NONLINEAR differential equations, *METRIC spaces, *BOUNDARY value problems, *FRACTIONAL differential equations, *MATHEMATICAL mappings
Abstract

In the present paper, we prove common fixed point theorems under different contractive mappings on C ★ -algebra-valued bipolar metric spaces. The results generalize and expand some well-known results from the literature. Examples and applications are given to strengthen our conclusion. Additionally, as an application of our results, we show that some classes of the nonlinear fractional differential equations with the boundary conditions have a unique common solution. [ABSTRACT FROM AUTHOR]

Published
2023
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50. The Study of Bicomplex-Valued Controlled Metric Spaces with Applications to Fractional Differential Equations.

Author

Mani, Gunaseelan, Haque, Salma, Gnanaprakasam, Arul Joseph, Ege, Ozgur, and Mlaiki, Nabil

Subjects
*FRACTIONAL differential equations, *METRIC spaces
Abstract

In this paper, we introduce the concept of bicomplex-valued controlled metric spaces and prove fixed point theorems. Our results mainly focus on generalizing and expanding some recently established results. Finally, we explain an application of our main result to a certain type of fractional differential equation. [ABSTRACT FROM AUTHOR]

Published
2023
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