Generalized R-Contraction by Using Triangular α-Orbital Admissible

Yıl 2021, Cilt: 10 Sayı: 1, 1 - 9, 30.04.2021

Ferhan Şola Erduran

Öz

This study presents Ciric type generalization of R-contraction and generalized R-contraction by using an α-orbital admissible function in metric spaces using the definition of R-contraction introduced by Roldan-Lopez-de-Hierro and Shahzad [New fixed-point theorem under R-contractions, Fixed Point Theory and Applications, 98(2015): 18 pages, 2015] and prove some fixed-point theorems for this type contractions. Thanks to these theorems, we generalize some known results.

Anahtar Kelimeler

α-admissible, R-contraction, Ciric generalization, Fixed point

Kaynakça

• S. Banach, Sur les operation dans les ensembles abstraits et leur application auxequeations integrales, Fundementa Matheaticae, 3, (1922) 133–181.
• W-S Du, F. Khojasteh, New results and generalizations for approximate fixed-point property and their applications, Abstract and Applied Analysis, 2014, (2014) Article ID: 581267, 1–9.
• E. Karapınar, E. Kumam, P. Salimi, On α-ψ-Meir Keeler contractive mappings, Fixed Point Theory and Applications, 2013, (2013) Article Number: 323, 1–21.
• O. Popescu, Some new fixed-point theorems for α-Geraghty contraction type maps in metric spaces, Fixed Point Theory and Applications, 2014, (2014) Article Number: 190, 1–12.
• H. Şahin, Best proximity point theory on vector metric spaces, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(1), (2021) 130–142.
• A. Meir, E. Keeler, A theorem on contraction mappings, Journal of Mathematical Analysis and Applications, 28, (1969) 326–329.
• F. Khojasteh, S. Shukla, S. Radenovic, A new approach to the study of fixed-point theory for simulation functions, Filomat, 29, (2015) 1189–1194.
• A. F. Roldan Lopez de Hierro, E. Karapınar, C. Roldan Lopez de Hierro, J. Martinez-Moreno, Coincidence point theorems on metric space via simulation functions, Journal of Computational Applied Mathematics, 275, (2015) 345–355.
• A. F. Roldan Lopez de Hierro, N. Shahzad, New fixed-point theorem under R-contractions, Fixed Point Theory and Applications, 2015, (2015) Article Number: 98, 1–18.
• M. Geraghty, On contractive mappings, Proceedings of the American Mathematical Society, 40, (1973) 604–608.
• I. A. Rus, Picard operators and applications, Scientiae Mathematicae Japonicae, 58, (2003) 191–219.
• B. Samet, C. Vetro, and P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Analysis: Theory, Methods & Applications, 75(4), (2012) 2154–2165.