## H. M. Srivastava, Amjad Ali, Aftab Hussain, Muhammad Arshad, Hamed Al Sulami, A certain class of $\theta_{L}$-type non-linear operators and some related fixed point results

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DOI: 10.23952/jnva.6.2022.1.05

Volume 6, Issue 1, 1 February 2022, Pages 69-87

Abstract. This paper presents a systematic investigation of an extension of the developments concerning the $\theta$-contractions, which were proposed in 2014 by Jleli and Samet. This paper generalizes the notion of the $\theta$-contractions to the case of non-linear $\theta_{L}$-contraction mappings, and prove multi-valued fixed point results in ${\mathfrak{b}}$-metric-like spaces. The paper also includes a tangible example, which displays the motivation for such investigations as those presented here. This paper is completed by giving an application of the proposed non-linear $\theta_{L}$-contractions to the Liouville-Caputo fractional derivatives and fractional differential equations.

H. M. Srivastava, Amjad Ali, Aftab Hussain, Muhammad Arshad, Hamed Al Sulami, A certain class of $\theta_{L}$-type non-linear operators and some related fixed point results, J. Nonlinear Var. Anal. 6 (2022), 69-87.