An Investigation of Extended Proinov Contraction under Non-Triangular Metric Structure and the Corresponding Applications
Main Article Content
Abstract
This article demonstrates several fixed point theorems of extended Proinov-type, on the existence and uniqueness of fixed points within the context of non-triangular metric spaces. Additionally, we provide two applications of our primary result, in solving existence and uniqueness of a solution for a non-homogeneous linear parabolic partial differential equation and a stochastic integral equation.
Article Details

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
References
Agarwal P, Jleli M, Samet B, Agarwal P, Jleli M, Samet B. JS-metric spaces and fixed point results. Fixed Point Theory in Metric Spaces: Recent Advances and Applications. 2018:139-53.
Gopal D, Agarwal P, Kumam P. Metric structures and fixed point theory. CRC Press; 2021.
Khojasteh F, Khandani H. Scrutiny of some fixed point results by S-operators without triangular inequality. Mathematica Slovaca. 2020;70(2):467-76.
Deshmukh A, Gopal D. Topology of nontriangular metric spaces and related fixed point results. Filomat. 2021;35(11):3557-70.
Karapınar E. Quadruple fixed point theorems for weak 𝜙-contractions. International Scholarly Research Notices. 2011;2011.
Karapınar E, Van Luong N. Quadruple fixed point theorems for nonlinear contractions. Computers & Mathematics with Applications. 2012;64(6):1839-48.
Khojasteh F, Shukla S, Radenović S. A new approach to the study of fixed point theory for simulation functions. Filomat. 2015;29(6):1189-94.
Roldán-López-de Hierro AF, Karapınar E, Roldán-López-de Hierro C, Martínez-Moreno J. Coincidence point theorems on metric spaces via simulation functions. Journal of computational and applied mathematics. 2015;275:345-55.
Jleli M, Samet B. A generalized metric space and related fixed point theorems. Fixed point theory and Applications. 2015;2015:1-14.
Jachymski J. Equivalent conditions for generalized contractions on (ordered) metric spaces. Nonlinear Analysis: Theory, Methods & Applications. 2011;74(3):768-74.
Achtoun Y, Radenović S, Tahiri I, Sefian ML. The nonlinear contraction in probabilistic cone b-metric spaces with application to integral equation. Nonlinear Analysis: Modelling and Control. 2024:1-12.
Proinov PD. Fixed point theorems for generalized contractive mappings in metric spaces. Journal of Fixed Point Theory and Applications. 2020;22(1):21.
Karapınar E, Martínez-Moreno J, Shahzad N, Roldan Lopez de Hierro AF. Extended Proinov 𝔛-contractions in metric spaces and fuzzy metric spaces satisfying the property NC by avoiding the monotone condition. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Serie A Matemáticas. 2022;116(4):140.
Karapinar E, Khojasteh F, Mitrović ZD, Rakočević V. On surrounding quasi-contractions on non-triangular metric spaces. Open Mathematics. 2020;18(1):1113-21.
Shahzad N, Hierro AFRLd, Khojasteh F. Some new fixed point theorems under (A, S)(A, S)-contractivity conditions. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales Serie A Matematicas. 2017;111:307-24.
Mlaiki N, Rizk D, Azmi F. Fixed points of (𝜓, 𝜙)− contractions and Fredholm type integral equation. Journal of Mathematical Analysis and Modeling. 2021;2(1):91-100.
Savaliya J, Gopal D, Srivastava SK, Rakočevič V. Search of minmal metric structue in the context of fixed poit theorem and corresponding operator equation. Fixed Point Theory;25(1).
Budhia L, Aydi H, Ansari AH, Gopal D. Some new fixed point results in rectangular metric spaces with an application to fractional order functional differential equations. Nonlinear Analysis: Modelling and Control. 2020;25(4):580-97.
Padcharoen A, Kumam P, Gopal D. Coincidence and periodic point results in a modular metric space endowed with a graph and applications. Creative Mathematics & Informatics. 2017;26(1).
Rao VSH. Topological methods for the study of nonlinear mixed stochastic integral equations. Journal of Mathematical Analysis and Applications. 1980;74(1):311-7.
Kazemi M, Deep A, Yaghoobnia A. Application of fixed point theorem on the study of the existence of solutions in some fractional stochastic functional integral equations. Mathematical Sciences. 2024;18(2):125-36.