New Fixed Point Theorems in Extended Orthogonal S-Metric Spaces of Type (µ, σ) with Applications to Fractional Integral Equations


Abstract views: 45 / PDF downloads: 32

Authors

  • Benitha wises Samuel Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India
  • Gunaseelan Mani Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India
  • Sabri T.M. Thabet Department of Mathematics, Radfan University College, University of Lahej, Lahej, Yemen
  • Imed Kedim Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
  • Miguel Vivas-Cortez Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, Pontifical Catholic University of Ecuador, Av. 12 de octubre 1076 y Roca, Apartado Postal 17-01-2184, Sede Quito, Ecuador

Keywords:

Extended S-metric Space of type (µ, σ);, Extended orthogonal S-metric Spaces of type (µ, σ), orthogonal metric space, S-metric space

Abstract

In this article, we propose the concept of extended orthogonal S-metric spaces of type (µ, σ) and explore several related
properties and theorems based on this concept. We provide examples to validate our findings. Finally, we illustrate the practical relevance of our results through applications to the fractional integral equations and Fredholm integral equation, highlighting the advantages of our findings.

References

Brouwer, L. Uber Abbildungen von Mannigfaltikeiten, Math. Ann. 1911, 13, 97–115.

Banach, S. Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fundam.

Math. 1922, 3, 133–181.

Sedghi, S. Shobe, N. Aliouche, A. A generalization of fixed point theorems in S-metric spaces, Mat.Vesnik. 2012, 64(3),

–266.

Sedghi, S. Dung, N.V. Fixed point theorems on S-metric spaces, Mat.Vesnik. 2014, 66(1), 113–124.

Sedghi, S.; Shobe, N.; Došenović, T. Fixed point results in S-metric spaces, Nonlinear Func. Anal. Appl. 2015, 20(1),

–67.

Kim, J.K. Sedghi, S. Gholidahneh, A. Rezaee, M.M. Fixed point theorems in S-metric spaces, East Asian mathematical

journal. 2016, 32, 677–684.

Mlaiki, N. Özgür, N.Y. Taş, N. New Fixed-Point Theorems on an S-metric Space via Simulation Functions, Mathematics.

, 7, 583.

Adewale, O.K. Iluno, C. Fixed point theorems on rectangular S-metric spaces, Scientific African. 2022, 16, 2468–2276.

Gordji, M.E. Rameani, M. De La Sen, M. Cho, Y.J. On orthogonal sets and Banach fixed point theorem, Fixed Point

Theory. 2017, 18, 569–578.

Gordji, M.E. Habibi, H. Fixed point theory in generalized orthogonal metric space, J. Linear Topol. Algebra. 2017, 6,

–260.

Senapati, T. Dey, L.K. Damjanović, B.A. New fixed results in orthogonal metric spaces with an application, Kragujev.

J. Math. 2018, 42, 505–516.

Gordji, M.E. Habibi, H. Fixed point theory in e-connected orthogonal metric space, Sahand Commun. Math. Anal.

, 16, 35–46.

Gungor, N.B. Turkoglu, D. Fixed point theorems on orthogonal metric spaces via altering distance functions, AIP Conf.

Proc. 2019, 2183, 040011.

Yang, Q. Bai, C.Z. Fixed point theorem for orthogonal contraction of Hardy-Rogers-type mapping on O-complete metric spaces, AIMS Math. 2020, 5, 5734–5742.

Sawangsup, K. Sintunavarat, W. Cho, Y.J. Fixed point theorems for orthogonal F-contraction mappings on O-complete

metric spaces, J. Fixed Point Theorey Appl. 2020, 22, 10.

Sawangsup, K. Sintunavarat, W. Fixed point results for orthogonal Z-contraction mappings in O-complete metric

space, Int. J. Appl. Phys. Math. 2020, 10, 33–40.

Gunaseelan, M. Arul Joseph, G. Park, C. Yun, S. Orthogonal F-contractions on O-complete b-metric space, AIMS

Mathematics. 2021, 6(8), 8315–8330.

Arul Joseph, G. Gunaseelan, M. Ege, O. Aloqaily, A. Mlaiki N. New Fixed Point Results in Orthogonal b-Metric Spaces

with Related Applications, Mathematics. 2023, 11(3), Article ID 677. https://doi.org/10.3390/math11030677

Ismat, B. Gunaseelan, M. Arul Joseph, G. Fixed Point of Orthogonal F-Suzuki Contraction Mapping on O-Complete

b-Metric Spaces with Applications, Journal of Function Spaces. 2021, 2021, 1–12.

Arul Joseph, G. Gunaseelan, M. Lee, J.R. Park, C. Solving a nonlinear integral equation via orthogonal metric space,

AIMS Mathematics. 2022 7(1), 1198–1210.

Gunaseelan, M., Arul Joseph, G., Javed, K., Kumar, S., On Orthogonal Coupled Fixed Point Results with an Application,

Journal of Function Spaces. 2022, 2022, 1–7.

Singh, B. Singh, V. Uddin, I. Acar, O. Fixed point theorems on an Orthogonal metric space using Matkowski type con-

traction, Carpathian Math. Publ. 2022, 14(1), 127–134.

Zeinab, E.D.D.O. Gordji, M.E. Davood, E.B. Banach fixed point theorem on incomplete orthogonal S-Metric Spaces, Int.

J. Nonlinear Anal. Appl. 2023, 2, 154–157.

Kamran, T. Samreen, M. UL Ain, Q. A generalization of b-metric space and some fixed point theorems, Mathematics.

, 5, 19.

Mlaiki, N. Extended Sb -metric spaces, J. Math.Anal. 2018, 9, 124–135.

Alqahtani, B. Fulga, A. Karapınar, E. Common fixed point results on an extended b-metric space, J. Inequal Appl.

, 158, 1–15.

Kushal, R. Sayantan, P. Mantu, S. Vahid, P. An Extended b-Metric-Type Space and Related Fixed Point Theorems

with an Application to Nonlinear Integral Equations, Advances in Mathematical Physics. 2020, 2020, 1–7.

Aydi, H. Muhammad, A. Dur-e-Shehwar, S. Samina, B. Rashid, A. Eskandar, A. Kannan-Type Contractions on New

Extended b-Metric Spaces, Journal of function spaces. 2021, 2021, 1–12.

Huang, H.; Singh, Y.M.; Khan, M.S.; Radenović, S. Rational Type Contractions in Extended b-Metric Spaces, Symmetry.

, 13, 614.

Nayab, A. Quanita, K. Hassen, A. Yaé, U. G. On Multivalued Fuzzy Contractions in Extended b-Metric Spaces, Journal

of Mathematics. 2021, 2021, 1–11.

Qaralleh, R. Tallafha, A. Shatanawi, W. Some Fixed-Point Results in Extended S-Metric Space of Type (m,s), Symmetry.

, 15, 1–11.

Mani, G. Haque, S. Gnanaprakasam, A.J. Ege, O. Mlaiki N. The Study of Bicomplex-Valued Controlled Metric Spaces

with Applications to Fractional Differential Equations, Mathematics. 2023, 11(12), 2742. https://doi.org/10.3390/

math11122742

Mani, G. Gnanaprakasam, A.J. Guran, L. George, R. Mitrović, Z.D. Some Results in Fuzzy b-Metric Space with b-Tri-

angular Property and Applications to Fredholm Integral Equations and Dynamic Programming, Mathematics. 2023,

, 4101. https://doi.org/10.3390/math11194101

Mani, G. Gnanaprakasam, A.J. Ege, O. Aloqaily, A. Mlaiki, N. Fixed Point Results in C*-Algebra-Valued Partial

b-Metric Spaces with Related Application, Mathematics. 2023, 11(5):1158. https://doi.org/10.3390/math11051158

Nallaselli, G. Gnanaprakasam, A.J. Mani, G. Mitrović, Z.D. Aloqaily, A. Mlaiki, N. Integral Equation via Fixed Point

Theorems on a New Type of Convex Contraction in b-Metric and 2-Metric Spaces, Mathematics. 2023, 11(2):344.

https://doi.org/10.3390/math11020344

Thirthar, A.A. Abboubakar, H. Alaoui, A.L. Sooppy Nisar, V. Dynamical behavior of a fractional-order epidemic model

for investigating two fear effect functions, Results in Control and Optimization. 2024, 16, 2666–7207.

Muthuvel, K. Kaliraj, K. Kottakkaran, S.N. Vijayakumar, V. Relative controllability for Ã-Caputo fractional delay

control system, Results in Control and Optimization. 2024, 16, 2666–7207.

Nisar, K.S. A constructive numerical approach to solve the Fractional Modified Cassama-Holm equation, Alexandria

Engineering. 2024, 106, 19–24.

S.T.M. Thabet, M.B. Dhakne, Nonlinear fractional integro-differential equations with two boundary conditions,

Advanced studies in contemporary mathematics, Vol. 26, No. 3, 513–526, 2016.

S.T.M. Thabet, M.B. Dhakne, M.A. Salman, R. Gubran, On Generalized Fractional Sturm-Liouville and Langevin

Equations Involving Caputo Derivative with Nonlocal Conditions, Progr. Fract. Differ. Appl., 6, No. 3, 225–237, 2020.

http://doi.org/10.18576/pfda/060306

Downloads

Published

2024-12-05

How to Cite

Samuel, B. wises, Mani, G., Thabet, S. T., Kedim, I., & Vivas-Cortez, M. (2024). New Fixed Point Theorems in Extended Orthogonal S-Metric Spaces of Type (µ, σ) with Applications to Fractional Integral Equations. Results in Nonlinear Analysis, 7(4), 146–162. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/509

Most read articles by the same author(s)