Generalized R-Contraction by Using Triangular α-Orbital Admissible

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.

Keywords:

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

PDF

___

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.

ISSN: 1304-7981
Yayın Aralığı: Yılda 3 Sayı
Başlangıç: 2012
Yayıncı: Tokat Gaziosmanpaşa Üniversitesi

Arşiv