Nonlinear Analysis and Computational Techniques

This book contains proceedings of select chapters presented at the International Conference on Nonlinear Analysis & Computational Techniques (ICNACT-2024), held at VIT Bhopal University, Madhya Pradesh, India, from 8 to 10 August 2024. It discusses advances, emerging trends and theoretical developments in topics related to nonlinear analysis and computational techniques, including the introduction to new function spaces, such as a generalized Orlicz with Rao and Ren’s norm, the s-Young space and the controlled G-metric spaces. The book explains some relationships among different types of near linear spaces and introduces the strongly λ-summable functions.

Nonlinear systems frequently require convergence and fixed point theorems. In this sense, the concept of q-lacunary almost statistical convergence is exposed. The book proposes a common coupled fixed point theorems, a few fixed point theorems for compatible mappings of type P and some applications on dynamic programming. In differential equations, some works extend Ostrowski-type inequalities; solution of the fractal nonlinear Klein–Gordon equation, study of a hybrid differential equation and the problem of exponential stability of the nonlinear Saint–Venant equation, finally provides a study of some properties for Cayley transform of operators. The book is useful to researchers in mathematics and applied sciences, engineers, graduate students, computational scientists, software developers and educators. They will benefit from this theory, which is essential for efficiently solving complex equations via the understanding, modeling and solving nonlinear problems and their theoretical and practical domains.

Hemanta Kalita is Assistant Professor, Mathematics Division, VIT Bhopal University, Kothri Kalan, Bhopal-Indore Highway, Sehore, Madhya Pradesh, India. A Ph.D. from Gauhati University under the guidance of Prof. Bipan Hazarika, he has an academic experience of 12 years and has worked in various capacity. With more than 35 research papers in peer-reviewed international journals and 2 papers in international conferences held in India and abroad, he has organized the International Conference (ICNAA-2022) at Assam Don Bosco University, and the International Conference on Nonlinear Analysis & Computational Techniques (ICNACT-2024) at VIT Bhopal University. An invited researcher at Usak University, Turkey, he has edited two issues of the Journal of Nonlinear and Convex Analysis as a Guest Editor, in 2023 and 2024.

Tomás Pérez Becerra is Professor-Researcher Director at the Technological University of Mixteca assigned to the Institute of Physics and Mathematics, Mexico. He is coordinator of the doctorate in mathematical modeling and is a member of the Center for Mathematical Modeling, Linkage and Consulting, Mexico. He has earned his degree in applied mathematics from the Autonomous University of Tlaxcala and a master’s degree and doctor of science from the Benemérita Universidad Autónoma de Puebla, Mexico, from which he graduated with honors and is a master in applied data science from the Institute of Executive Education. He carried out two research stays at the National Institute of Education of the Nanyang Technological University in Singapore and has two post-doctorates at the Mixteca Technological University.

Kiran Kumar Behera has been actively associated with the Mathematics Training and Talent Search Programme (MTTS) under the National Board of Higher Mathematics (NBHM), India. A doctorate in mathematics and master’s in applied mathematics from the IIT Roorkee, he has more than four years of postdoctoral experience working in IISc Bangalore and NISER Bhubaneswar. A recipient of the Dr. D.S. Kothari fellowship and the NBHM postdoctoral fellowships, he has published six research articles in peer-reviewed international journals and attended several conferences and workshops. His research interests include orthogonal functions and kernel methods in data analysis.