Fixed point theorems for generalized orthogonal F-contraction and F-expansion of Wardowski kind via the notion of $\psi-$fixed point

Document Type : Research Paper

Authors

1 Department of Mathematics, K.R.M.D.A.V. College, Nakodar, Punjab, 144040, India

2 Department of Mathematics, Om Sterling Global University, Hisar, Haryana, 125001, India

Abstract

In this manuscript, we introduce generalized orthogonal ($\mathfrak{f^{*}}, \psi)$-contraction of kind (S) and use this concept to establish $\psi$-fixed point theorems in the frame of O-complete orthogonal metric space. Secondly, we introduce the new notion of generalized orthogonal ($\mathfrak{f^{*}}, \psi)$ expansive mapping and utilize the same to prove some fixed point results for surjective mapping satisfying certain conditions. Our results extend and improve the results of  [3] and [7] by omitting the continuity condition of $F\in \Im$ with the aid of $\psi$-fixed point. We also give an illustrative example which yields the main result. Also, many existing results in the frame of metric spaces are established.

Keywords

[1] N.V. Dung and V.L. Hang, A fixed point theorem for generalized F-contractions on complete metric spaces, Vietnam J. Math 43 (2015), 743–753.

[2] M.E. Gordji, M. Rameani, M. Sen and Y.J. Cho, On orthogonal sets and Banach fixed point theorem, Fixed Point Theory 18 (2017), 569–578.

[3] J. Gornicki, Fixed point theorems for F-expanding mappings, Fixed Point Theory Appl. 9 (2017), 1–10.

[4] M. Jleli, B. Samet and C. Vetro, Fixed point theory in partial metric spaces via φ-fixed point concept in metric spaces, J. Inequal. Appl. 426 (2014), no. 1, 1–9.

[5] M. Kumar and S. Arora, Fixed point theorems for modified generalized F-contraction in G-metric spaces, Bol. Soc. Paran. Mat (2019) 1-8 doi: 10.5269/bspm.45061.

[6] P.P. Murthy and K.V. Prasad, Weak contraction condition involving cubic terms of d(x, y) under the fixed point consideration, J. Math. 2013 (2013), Article ID 967045, 1–5.
 
[7] H. Piri and P. Kumam, Wardowski type fixed point theorems in complete metric spaces, Fixed Point Theory Appl. 45 (2016), 1–12.

[8] T. Senapati, L.K. Dey, B. Damjanovic and A. Chanda, New fixed point results in orthogonal metric spaces with an application, Kragujevac J. Math. 42 (2018), no. 4, 505–516.

[9] P. Shahi, J. Kaur, and S.S. Bhatia, Fixed point theorems for (ξ, α)-expansive mappings in complete metric spaces, Fixed Point Theory Appl. 157 (2012) 1-12.

[10] A. Taheri and A.P. Farajzadeh, A new generalization of α-type almost-F-contractions and α -type F-Suzuki contractions in metric spaces and their fixed point theorems, Carpathian Math. Publ. 11 (2019), 475–492.

[11] Y. Touaila and D. Moutawakila, Fixed point theorems on orthogonal complete metric spaces with an application, Int. J. Nonlinear Anal. Appl. 12 (2021), 1801–1809.

[12] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 94 (2012), 1–11.

[13] D. Wardowski and N.V. Dung, Fixed points of F-weak contractions on complete metric spaces, Demonst. Math. XLVII (2014), 146–155.
Volume 14, Issue 2
February 2023
Pages 221-231
  • Receive Date: 14 July 2022
  • Revise Date: 07 September 2022
  • Accept Date: 11 September 2022