Solution of non linear matrix equation using $\theta$-hyperbolic sine distance functions

Reena Jain

doi:10.5269/bspm.82105

Reena Jain VIT Bhopal University

Abstract

In this paper we introduce Ciric-type(I) $\theta$-hyperbolic $\mathcal{Z}$- contraction and discuss the existence and uniqueness of fixed point of a mapping satisfying Ciric-type(I) $\theta$-hyperbolic $\mathcal{Z}$- contraction in the setting of orbitally complete metric spaces. We furnish the result by suitable example. Further we apply the results to find solution of non liner matrix equation.

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References

D. Aronov, Fast algorithm for the metric-space analysis of simultaneous responses of multiple single neurons, J. Neurosci. Meth., 124 (2023), 175–179. https://doi.org/10.1016/S0165 0270(03)00006-2

A. L. Gibbs, Convergence in the Wasserstein metric for Markov chain Monte Carlo algorithms with applications to image restoration, Stoch. Models, 20(2004), 473–492. https://doi.org/10.1081/STM-200033117

E. Vidal, H. M. Rulot, F. Casacuberta, J. M. Benedi, On the use of a metric-space search algorithm (AESA) for fast DTW-based recognition of isolated words, IEEE Trans. Acoust. Speech Signal Process., 36 (1988), 651–660. https://doi.org/10.1109/29.1575

S. G. Matthews, Partial metric spaces, A. NY. Acad. Sci., 728 (1994), 183–197. https://doi.org/10.1111/j.1749-6632.1994.tb44144.x

M. B. Smyth, Completeness of quasi-uniform and syntopological spaces, Lond. Math. Soc., 49 (1994), 385–400. https://doi.org/10.1112/jlms/49.2.385

M. Jleli, B. Samet, On-hyperbolic sine distance functions and existence results in complete metric spaces, AIMS Mathematics, 9(10): 29001–29017. https://doi: 10.3934/math.20241407

S. H. Cho, Fixed Point Theorems for Ciric Type Z-Contractions in Generating Spaces of Quasi-Metric Family, Journal of Function Spaces Volume 2019, Article ID 8290686, 1-8.

Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289–297

R. Kannan, Some results on fixed points, Bull. Calc. Math. Soc., 60 (1968), 71–76. https://doi.org/10.2307/2316437

L. Ciric, A generalization of Banach’s contraction principle, P. Am. Math. Soc., 45 (1974), 267 273. https://doi.org/10.1090/S0002-9939-1974-0356011-2

A. Meir, E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl., 28 (1969), 326–329. https://doi.org/10.1016/0022-247X(69)90031-6

J. Caballero, J. Harjani, K. A. Sadarangani, Fixed point theorem for operators of Meir-Keeler type via the degree of nondensifiability and its application in dynamic programming, J. Fixed Point Theory A., 22 (2020), 13. https://doi.org/10.1007/s11784-019-0748-1

F. Khojasteh, S. Shukla, S. Radenovic, A new approach to the study of fixed point theory for simulation functions, Filomat, 29 (2015), 1189–1194. https://doi.org/10.2298/FIL1506189K

A. Chanda, L. K. Dey, S. Radenovic, Simulation functions: A survey of recent results, RACSAM Rev. R. Acad. A, 113 (2019), 2923–2957. https://doi.org/10.1007/s13398-018-0580-2

B. Samet, C. Vetro, P. Vetro, Fixed point theorems for–contractive type mappings, Nonlinear Anal., 75 (2012), 2154–2165. https://doi.org/10.1016/j.na.2011.10.014

I. Kedim, M. Berzig, Fixed point theorems for Maia contractive type mappings with applications, J. Math. Anal. Appl., 504 (2021), 125381. https://doi.org/10.1016/j.jmaa.2021.125381

S. Pakhira, S. M. Hossein, A new fixed point theorem in Gb-metric space and its application to solve a class of nonlinear matrix equations, J. Comput. Appl. Math., 437 (2024), 115474. https://doi.org/10.1016/j.cam.2023.115474

Doaa Filali, Mohammad Dilshad, Mohammad Akram, Mohd. Falahat Khan, Syed Shakaib Irfan, Hybrid inertial viscosity-type forward-backward splitting algorithms for variational inclusion problems, 2025, 10, 2473-6988, 28829, 10.3934/math.20251269

Mohammad Dilshad, Mohammad Akram, Md. Nasiruzzaman, Doaa Filali, Ahmed A. Khidir,nAdaptive inertial Yosida approximation iterative algorithms for split variational inclusion and fixed point problems, AIMS Mathematics, 8(6): 12922–12942. DOI: 10.3934/math.2023651

A. Das, M. Rabbani, S. A. Mohiuddine, B. C. Deuri, Iterative algorithm and theoretical treatment of existence of solution for (k, z)-Riemann-Liouville fractional integral equations, J. Pseudo-Differ. Oper. Appl. (2022) 13:39.

A. Das, S. A. Mohiuddine, A. Alotaibi, B. C. Deuri, Generalization of Darbo-type theorem and application on existence of implicit fractional integral equations in tempered sequence spaces, Alexandria Eng. J. 61 (2022) 2010-2015.

S. A. Mohiuddine, A. Das, A. Alotaibi, Existence of solutions for nonlinear integral equations in tempered sequence spaces via generalized Darbo-type theorem, J. Funct. Spaces 2022 (2022) 4527439, pp8.

S. A. Mohiuddine, A. Das, A. Alotaibi, Existence of solutions for infinite system of nonlinear q-fractional boundary value problem in Banach spaces, Filomat 37(30) (2023) 10171-10180.