A Suprametric Framework for \(\Theta\)-Contractions with Application to the Fourth-Order Euler-Bernoulli Beam Equation
Applicable Nonlinear Analysis, Volume 3, Issue 3, December 2026, Pages: 176–194
Haroon Ahmad
Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan
Zai-Yun Peng
School of Mathematics, Yunnan Normal University, Kunming, 650092, P.R. China
Adrian Petruşel
Department of Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
Jen-Chih Yao
Center for General Education, China Medical University, Taichung 406040, Taiwan
Abstract
This manuscript offers a comprehensive study of \(\Theta\)-contractions, thereby demonstrating both the existence and uniqueness of fixed points results in the setting of complete suprametric spaces. We present an example that satisfies the proposed contraction conditions in a suprametric space, but not in a standard metric space. Moreover, the example illustrates the proposed contraction while demonstrating that the Banach contraction fails, highlighting the novelty of our approach. Then we employ our main result to a fourth-order Euler–Bernoulli beam equation with clamped–clamped boundary value problem. By transforming the original problem into an integral equation, which shows that the solution operator maintains the proposed contraction properties within a complete suprametric space. This study significantly expands fixed point theory beyond its usual application in metric spaces. This provides a strong framework for both theoretical analysis and practical problem-solving in nonlinear contexts.
Cite this Article as
Haroon Ahmad, Zai-Yun Peng, Adrian Petruşel, and Jen-Chih Yao, A Suprametric Framework for \(\Theta\)-Contractions with Application to the Fourth-Order Euler-Bernoulli Beam Equation, Applicable Nonlinear Analysis, 3(3), 176–194, 2026