New Coincidence and Fixed Point Theorems via a New Simulation Function Technique in Metric Spaces

Abderrahmane Boudraa; Taieb Hamaizia

doi:10.5281/zenodo.17092204

New Coincidence and Fixed Point Theorems via a New Simulation Function Technique in Metric Spaces

Abderrahmane Boudraa

System Dynamics and Control Laboratory, Department of Mathematics and Informatics, Larbi Ben M’Hidi University, Oum-El-Bouaghi, 04000, Algeria.

Taieb Hamaizia

System Dynamics and Control Laboratory, Department of Mathematics and Informatics, Larbi Ben M’Hidi University, Oum-El-Bouaghi, 04000, Algeria.

Received: 12 Jul 2025 | Accepted: 26 Jul 2025 | Final Version: 31 Aug 2025

Abstract

In this paper, we present enough conditions for the existence and uniqueness of coincidence points based on simulation functions in metric spaces. We present which generalizes and unifies several classic fixed point theorems. We supplement the main results with sample examples and corollaries that illustrate the applicability as well as the effectiveness of the theoretical results.

Keywords:

Complete Metric space, Generalized contraction, Simulation function, Fixed point.

1. Introduction

Fixed point theory is an eminent sub-field within nonlinear functional analysis since Banach's theorem when he established the existence and uniqueness of fixed points under specified conditions...

References

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Banach S. Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund Math 1922; 3: 133–181.
Cvetkovic E, Karapinar E, Rakocevic V. Fixed point results for admissible ℤ-contraction. Fixed Point Theory 2016; 2: 515–526.
Cvetkovic M, Karapinar E, Rakocevic V. Fixed point results for admissible ℤ-contractions. Fixed Point Theory 2018; 19: 515–526.
Hamaizia T, Beloul S. Common fixed point result for generalized α*-ψ-contraction for C-class function in b-metric spaces. Ann Commun Math 2021; 4(2): 155–163.
Karapinar E. Fixed points results via simulation functions. Filomat 2016; 30(8): 2343–2350.
Merdaci S, Hamaizia T. New common fixed point theorem for multi-valued mappings in b-metric spaces. Asia Mathematika 2023; 7(2): 1–12.
Padcharoen A, Kumam P, Saipara P, Chaipunya P. Generalized Suzuki type ℤ-contraction in complete metric spaces. Kragujevac J Math 2018; 42(3): 419–430.
Prudhvi K. Results on fixed points for WC-mappings satisfying generalized contractive condition in C-metric spaces. Asia Mathematika 2024; 8(1): 112–117.
Radenovic S, Chandok S. Simulation type functions and coincidence points. Filomat 2018; 32(1): 141–147.
Radenovic S, Vetro F, Vujakovic J. An alternative and easy approach to fixed point results via simulation functions. Demonstr Math 2017; 50: 223–230.
Roldan-Lopez-de-Hierro AF, Karapinar E, Roldan-Lopez-de-Hierro C, Martinez-Moreno J. Coincidence point theorems on metric spaces via simulation functions. J Comput Appl Math 2015; 275: 345–355.
Shatarah A, Ozer O. A kind of fixed point theorem on the complete C*-algebra valued s-metric spaces. Asia Mathematika 2020; 4(1): 53–62.
Singh MR, Singh YM. On various types of compatible maps and common fixed point theorems for non-continuous maps. Hacettepe J Math Stat 2011; 40(4): 503–513.

[1] Alghamdi MA, Gulyaz-Ozyurt S, Karapinar E. A note on extended ℤ-contraction. Mathematics. 2020; 8: 1–14.

[2] Banach S. Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund Math 1922; 3: 133–181.

[3] Cvetkovic E, Karapinar E, Rakocevic V. Fixed point results for admissible ℤ-contraction. Fixed Point Theory 2016; 2: 515–526.

[4] Cvetkovic M, Karapinar E, Rakocevic V. Fixed point results for admissible ℤ-contractions. Fixed Point Theory 2018; 19: 515–526.

[5] Hamaizia T, Beloul S. Common fixed point result for generalized α*-ψ-contraction for C-class function in b-metric spaces. Ann Commun Math 2021; 4(2): 155–163.

[6] Karapinar E. Fixed points results via simulation functions. Filomat 2016; 30(8): 2343–2350.

[7] Merdaci S, Hamaizia T. New common fixed point theorem for multi-valued mappings in b-metric spaces. Asia Mathematika 2023; 7(2): 1–12.

[8] Padcharoen A, Kumam P, Saipara P, Chaipunya P. Generalized Suzuki type ℤ-contraction in complete metric spaces. Kragujevac J Math 2018; 42(3): 419–430.

[9] Prudhvi K. Results on fixed points for WC-mappings satisfying generalized contractive condition in C-metric spaces. Asia Mathematika 2024; 8(1): 112–117.

[10] Radenovic S, Chandok S. Simulation type functions and coincidence points. Filomat 2018; 32(1): 141–147.

[11] Radenovic S, Vetro F, Vujakovic J. An alternative and easy approach to fixed point results via simulation functions. Demonstr Math 2017; 50: 223–230.

[12] Roldan-Lopez-de-Hierro AF, Karapinar E, Roldan-Lopez-de-Hierro C, Martinez-Moreno J. Coincidence point theorems on metric spaces via simulation functions. J Comput Appl Math 2015; 275: 345–355.

[13] Shatarah A, Ozer O. A kind of fixed point theorem on the complete C*-algebra valued s-metric spaces. Asia Mathematika 2020; 4(1): 53–62.

[14] Singh MR, Singh YM. On various types of compatible maps and common fixed point theorems for non-continuous maps. Hacettepe J Math Stat 2011; 40(4): 503–513.